My understanding is that on average there are differences in psychology between conservative and progressive people. For example, conservative people tend to be okay with unfairness, since from their point of view society is a hierarchy and of course the people at the top are better off.
Anyway, given that conservative and progressive people have a different vision of an ideal society and also different ideas about how to get there, it is reasonable to expect them at act differently. We know that most politically motivated violence is from the right.