It's true that no white person currently alive today (In the Anglosphere) owns slaves (unless you run a prison or are a CEO, but that's another discussion for another day) and only a minority (*perhaps 'minority' is generous, but whatever*) are outwardly racist but it's true that every white person alive today benefits from white privilege, and the concept of white privilege can be traced back to the roots of slavery.

Slavery wasn't your fault. Colonialism was not your fault. You should not feel personally guilty for it. I certainly feel bad that my society had committed such terrible acts, but I am not personally responsible for those things. However, being ignorant to privilege or inadvertedly reinforcing white supremacist social structures can be your fault and it can cause damage to equality progress.

I consider myself to be a relatively poor, working-class white person; that means that I have white privilege, but I don't have as many economic privileges as - for the sake of argument - a black person whom is paid more than me. Etc.

So, while no white person alive today is directly responsible, by their inaction in dismantling the concept of white privilege they are in a way complicit. 

Even if you yourself don't commit any racist or discriminatory actions, even if you do something like burying your head in the ground and saying you are "colourblind" or "don't see race" is a statement coming from and reinforcing white privilege, even if it's not directly discriminatory against others in and of itself.

It is a complex concept that is a little difficult to wrap your head around - as a white person, it sure was for me - but it doesn't hurt. 

I find that viewing my actions through this lens allows me to inadvertedly avoid offending others, and also helped me understand why certain statements are racist due to an underlying meaning rather than the meaning of the words themselves. 

For an example, "It's OK to be white" isn't a directly racist statement, but it was organized and popularized by racist groups, so by repeating that phrase you are indirectly spreading a message that originated from racists with the overt idea of pushing a specific narrative - therefore, it is racist.

Conscientiousness costs nothing. Don't take making a mistake personally. If you're called out, change your behaviour, learn, and move on.