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.
Anton Maegerle
Some Conservatives accuse Maegerle's work of containing a leftist bias because he makes nearly no distinction between Conservatives and Nazis, and criticize that he receives public money for this. For example, Maegerle defends the use of political correctness, and published an article in the left-wing newspaper "Jungle World" during the German federal election, 2002 in which he, as a SPD member, accused CDU chancellor candidate Edmund Stoiber of having ""best ties to the twillight zone of right-wing extremism"". The extremism researcher Eckhard Jesse has criticized Maegerle for "scent[ing] in the well-known Antifa manner almost everywhere right-wing extremists."