Varieties of criticism
Conservative criticism has nothing much to do with "left-wing" or "right-wing", because left-wing people are often very conservative, in the defined sense, while right-wing people can also be very radical, in the defined sense. The difference between "radical" and "conservative" has more to do with the belief in whether "a change to something genuinely new" is really possible and necessary. Radicals typically believe strongly that such change is highly desirable and necessary, and that it can be achieved. Their criticism is that there is "not enough" change. Conservative critics, by contrast, are very skeptical about any such change, because they feel the change is really "just another form" of something that already exists.
Right-wing authoritarianism
Altemeyer suggested that authoritarian politicians are more likely to be in the Conservative or Reform party in Canada, or the Republican Party in the United States. They generally have a conservative economic philosophy, are highly nationalistic, oppose abortion, support capital punishment, oppose gun control legislation and do not value social equality. The RWA scale reliably correlates with political party affiliation, reactions to Watergate, pro-capitalist attitudes, religious orthodoxy and acceptance of covert governmental activities such as illegal wiretaps. Although authoritarianism is correlated with conservative political ideology, not all authoritarians are conservative and not all conservatives are authoritarian. It is also worth noting that many authoritarians have no interest in politics.