Well, I see you’ve added the “generally” qualifier, but I don’t think I can accept this sentence as written.
While it is true that individuals can choose their own path, decide when and where they will be, and to some degree to whom they will listen, an environment with visible, encouraged and consistent “activism” absolutely will have an impact on a person, especially a person trying to avoid it.
The route to class, the opportunities for casual social interaction, the nature of sanctioned and non sanctioned school events and speakers, the social pressure associated with one’s new peers - all these and more have the potential to disrupt the choices and experiences of someone.
We can discuss whether it is “good” or “bad” or “neither”, and also “how much it matters”, but I think the potential impact is there, and is as much a consideration of fit as is the weather or the bathroom arrangement in the dorms.
In answer to the original question, again in very general terms … large research institutions, usually public, would trend toward the least politically active, and also would have that activism diluted by shear size…