>

The devil is, of course, in the details, but that doesn’t mean that these labels are in and of themselves toxic. They are useful as a shorthand to describe your own or someone else’s political positions broadly. No one arguing in good faith would assume any individual dogmatically adheres to every position associated with these labels just because they use it to quickly summarize their political beliefs. 
Also, not everyone who disagrees with you or downvotes you is toxic.
It dates back to the French Revolution and the National Assembly. Those who wanted to retain more traditional elements in the new constitution (i.e. the more conservative) would sit on the right hand side of the assembly, while those who wanted more radical reform would sit on the left hand side. >

Huh. Thanks. I never knew that. >

Believe it or not it hasnt always been this way. Social progressive stances historically were found in both parties and so were socially conservative ones. In fact for most of American history the greatest indicator of social stances and policies wasnt your party but rather where you lived geographically (with the south and rural midwest being dominated by conservatives and urban coasts and Northeast dominated by Progressives). Your political party was usually more of an indicator of economic policies you supported. Depending on what period of American history youre talking about Republicans have always traditionally been in favor of big business interests, in the past they wanted to use income for the government on internal improvements like railroads while democrats wanted to use revenue to reduce taxes and tarrifs and usually they supported inflationary policies like the silver dollar and greenbacks.
Many of Americas most notable progressives were actually Republicans like Theodore Roosevelt who was anti trust and in favor of policies like the 8hr work week aminimum wage banning child labor etc. In 1912 however the Republicans backed Taft, Teddys successor, who represented the conservative wing of the party and thus began the process of many progressives leaving the republican party. (Remember this process happened very slowly and even later on youd still have Republicans like Eisenhower who were very much in favor of a welfare social safety net 40 years later).
Anyways, remember when I mentioned Democrats embraced inflationary policies? That was around the time they merged with the populists party and in general Dems were more pro union (since they believed unions and companies needed to settle workers rights issues rather than rhe government doing so). Well combine that with progressives leaving the Republican party and a Great Depression and you get: FDR. FDR is pretty much as close as ypull ever get to a socialist American president. His New Deal brought out tons of social welfare programs to deal with the depression, he reshapes the Democratic party, then his successor Truman desegregates the federal govt (something that was first put in place by another Dem president Wopdrow Wilson). Eisenhower also takes a role in favor of civil rights but the guy frankly was appealing to members of both parties anyways. So FDR is what made the Democrats into the leftist party leaving the GOP as the capitalist or right wing party. Then in the 60s Lyndon B Johnson passes the Civil Rights Act of 1964 (there were others before this but this is the one that matters). Conservative Democrats break from the party to become the Dixiecrats who get swooped up over time by the GOP thanks to the southern strategy. Meanwhile social progressives had been slowly leaving the party and moving towards the Dems for decades. Even Black voters had moved from the party if Lincoln to FDR (because of his pro union stance) and cause of Johnson. By the time you get Reagan in the 80s we have our modern political system in America. The GOP had purged out its progressives and they went to the Dems and the Dems increasingly progressive social stances caused its own Conservatives to walk out on them amd join the GOP. As a result you now have the two parties of today who are more polarized than they have ever been in US history. I hope this answered your question, I know its a lot but you said you werent American and so I wanted to give as much context as possible. >

Thanks, the insight provided in this comment is much higher than most of the other top-level comments. >

This is a question about what words mean.
During the French Revolution, the National Assembly was divided between supporters of the king and church, who sat on the right, and the supporters of liberty equality and fraternity, who sat on the left.  That was the origin of the left-vs-right thing in politics.  
How I see it, those who want to preserve an existing social hierarchy (or restore an earlier one) are on the right, those who want to flatten or do away with a social hierarchy are on the left.  These line up pretty well with whatever notions I use the words "conservative" and "progressive" to mean.  You haven't defined any of these words as you use them so I don't know how well this matches your own thinking. >

That maybe where the "right' and "left" nomenclature began, but the terms "conservative" and "right wing" have dramatically shifted in connotation. Well, the politics have as well which accounts for it. However, 30 yrs ago 'conservative" was much more about common sense solutions to every day issues: fiscal responsibility, less foreign entanglements, etc. It did not mean foaming at the mouth slandering Democrats and holding up bills that would serve the people. Yes there's always been that sort of nonsense, no it was not like this day and age of blatant disregard for the public needs. >

I don’t think this is quite accurate. The postwar American conservative movement started accelerating in power in the 1960s and 1970s not because of a “fiscal responsibility” platform, but because of opposition to the Civil Rights Act, desegregation, and liberal gains of the Warren court era. The racial politics of Trump and the tea party aren’t new, nor are they a departure from conservative dogma. I’m not sure where the idea that conservatives used to be more reasonable came from, but it‘s not supported by American history. >

You aren't wrong.
It seems that the current GOP wants to go back to that. When I was a kid, being a conservative in the 80's did not mean "racist, sexist, religious gun toting totalitarian". 
There was a period of time when "conservative" was a sensible option in politics. 
I left the GOP when the Tea Party started what we have now. >

I don’t know, I mean Reagan was certainly participating in the “racist, sexist, religious” stuff at the very least. 
I don’t think the modern conservative movement can be separated from that. It’s fundamentally a reaction to egalitarianism. I completely agree that the rhetoric has changed, it’s become more vulgar, but I think that the underlying motivating factors are mostly the same. >

They've always been the same since abolitionists and the civil war. It's all about the societal norm that has shifted to constant rage bait that is dismayingly dividing the country.
There was a minute when the sexist racist elitist sort had the understanding that society did not accept them as "good" for the people. They were in the shadows. 
Now it's "grab em by the p*$$y" and guns at protests and "bodily autonomy for those that agree with pseudo christianity" and no civil discourse on resolving things that actually matter.
Sigh. Whatever. It's all just going to burn away. >

You’re right, there definitely was a period where open bigotry was far more frowned upon. It’s hard to imagine Bush Sr, engaging in it for example. >

related question - before the civil rights movement or in the civil war (when the parties of the US had quite different alignments) - did the democrats ever see themselves as 'conservatives'? >

Yes, they were considered the more conservative party until the Civil rights Era. >

The Dems moved to the left of the Republicans on economic issues and government programs during the New Deal era.  Some of the Southern Democrats remained extremely conservative during this period, others supported New Dealism but largely remained terrible on race, so it was a mixed bag.
The Northern Democrats became largely to the left of Northern Republicans after this, although some progressive Republicans supported the New Deal and hung on awhile longer. >

Yep. The Southern Democrats supported the economic legislation of the New Deal. That's why the New Deal did not benefit African Americans. That's why the Great Society was a relative failure, because racist white Southerners couldn't stand to see African Americans to take welfare benefits. >

In the US "conservative" sounds more or less like it is: not changing, embracing old and established ways. It's a sheisty way to say "I don't want minorities or women to have any power" or otherwise fight any Progressivism. American Conservatives want things to stay the way they used to be, when white males from prosperous families or Corporate America Elite made all the decisions. This ensures that profits continue to funnel upwards to the Robber Barons, Oligarchs, and Power Mavens. Labor Unions and Progressive or Liberal political action counter this predation but only with active support from the prey, i.e. you and me. >

Prior to the 1950's, Right-wing meant Social Hierarchy. Left-wing meant Social Equality. This was born out of the French Revolution and became the foundation of European politics.
It should be noted that this was completely foreign to Americans until the 1920's, but even then it was rarely used to classify US parties. Socialist writers used the terms when writing about European politics, but it was very rarely used by Americans.
In the US, political positions were simply classified by Parties since parties were ideological (Democrats supported Agrarianism, Republicans supported Industrialization, Whigs supported free markets). It didn't really make sense anyway since all of these would have been classified as Left-wing or anti-Right (they all opposed Monarchism and Western Civilization).
The 1950's brought the Red Scare to America, and it was conspiracy theorists and anti-Communists who adopted the Right-wing concept. They simply believed that being an anti-Communist made you a Rightist, when in reality a Constitutional Democratic Republic that guarantees individual rights to the masses is inherently a Left-wing concept.
Notably, it was the John Birch Society that popularized the term "Right-wing" in America. It then went mainstream by William F. Buckley Jr. who also had a political war to purge the conspiracy nuts from the Republican Party while driving out the New Deal Republicans like Eisenhower, Nixon, and Rockefeller. Nixon managed to succeed after Goldwater failed in his election. It wasn't until Reagan that Buckley secured the party for the "New Right" who he classified as free market and Christian conservative. >

Conservatism has always resided on the right side of the political spectrum. The 2022 brand of conservatives does not align with the political ideology - todays right wing is far right bordering on fascism. >

Supply-side, nationalist vs. Laber/demand, humanist; conservative vs. liberal. In the US, people who blame victims and award predators are Republican; people who see the systemic injustice in our country are Democrats. >

'twas ever thus. Ask yourself which aspects of society Conservatives wish to conserve. >

There's a kind of linguistic smear ("smear" as in "to smudge," not as in "to denigrate") that happens over time.
A lot of political terms tend to have region or country specific meanings within their own political context. 
IE: I'm an anarchist in the US. If I was to say "libertarian socialist," that would mean something different here as opposed to saying it in Europe. A "libertarian" also means radically different things in both places.
In a US context, the dichotomy between conservative and "right-wing" isn't necessarily synonymous but the terms do get used interchangeably in popular parlance, often (but not always) as a way to insult that political group. It's an effort to marginalize certain people by painting their views as "off the table" in terms of political discourse.
There is also ideological crossover between people who would identify as conservative and right-wing such that the lines between the two aren't exactly clearly drawn.

Being conservative doesn't have to be the same as being right-wing. In a situation where a left-wing government is changing to a right-wing one, conservative would probably be associated with left-wing (and progressive would be associated with right-wing).

It doesn't have to but it does often result in "fellow travelers" wherein someone who is more conservative, though they may not agree 100% with someone who is outwardly right-wing, is willing to tolerate/support the right-winger because they agree on a certain point that the conservative values the support on. In your example, a conservative person might not love a right-wing government but they're far more likely to support it if the current government is left-wing.

The demarcation I usually refer to is the issue of change - how do you view political change?
On the left, I look at radical leftists, leftists, progressives, and liberals.
Liberals are people who are pretty much happy with the status quo. They believe in some reforms but nothing major and almost exclusively through extant systems of redress.
Progressives are a lot less happy with the status quo but, by and large, seek change through means that are more conciliatory to state power. They fundamentally appeal to systems of power for change but are willing to do so primarily through "official" channels. Progressives will protest, block traffic, etc but when they're told to go home they will and the primary focus of their efforts is legal reform.
Leftists support the drastic change of state power to the extent you might call it revolutionary but they seek these changes by manipulating extant levers of power. These are your demsocs/socdems, some Socialists, etc. For leftists, the state must be dismantled but this can be done by using the tools used to build it. Leftsts are not generally in favor of reform as a primary goal though they will seek it as a means to create change towards a goal state. 
Radical leftists eschew any notion that reform is possible and seek radical change outside the umbrella of state control. This does not inherently mean violence but radical leftists are the most likely people on the broad left to be willing to throw hands. The key idea for the radical left is the state is beyond reform and that it should be the political goal to build something else instead.
The progression is moving further and further away from a support of the status quo and of change via available avenues to participate in state sanctioned reform.
That is broadly mirrored on the right with the minor exception that you don't have that many people on the right who are completely against the idea of a state period. They may favor a very small, weak state but they support some kind of governmental structure. >

Well you are going by the book and it doesn't really help that USA is for all practical purposes a 2 party system.
So when some republicans say that global warming is a hoax or   earth is 6000 years old, or vaccines are dangerous, or we love guns .... There is no room left for somebody who opposes gun control but supports women's right to choose in that party. 
What I mean is, USA does not lack a political spectrum, but it certainly lacks the formal representation of the spectrum. They are binary, or at least that is what it looks to a non American like me. >

It seems like modern fascists started hiding behind the conservative moniker and progressive or liberals were eager to let them hoping they would pull more people to their side in the resultant polarization. No words don’t mean anything anymore which is what the fascists wanted in the first place and we are all worse off >

Labels like "left" and "right", and even "progressive" and "conservative" to a slightly lesser extent, are toxic to political discourse. They're practically meaningless and only serve to encourage groupthink and tribalism. We'd all be better off if everyone just stopped using them and discussed specific ideas and policies instead.
As usual, toxic people will downvote this but won't explain why they think I'm wrong.