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.
Conservatism
According to psychologist Bob Altemeyer, individuals who are politically conservative tend to rank high in right-wing authoritarianism (RWA) on his RWA scale. This finding was echoed by Theodor Adorno. A study done on Israeli and Palestinian students in Israel found that RWA scores of right-wing party supporters were significantly higher than those of left-wing party supporters. However, a 2005 study by H. Michael Crowson and colleagues suggested a moderate gap between RWA and other conservative positions: "The results indicated that conservatism is not synonymous with RWA".