Simply because an area of study and society share the same orthodoxies, I wouldn't say that's sufficient to qualify as research being agenda-driven, though maybe you could say there's a pressure to operate under a certain agenda, all sciences face the same in that scientists must first decide what to study before they study it, and as such based on the probabilities they can reckon with (being clever people) they can tell if something will lead to a "good" or a "bad" result. In fact, a recent study of submissions in
Nature found that very few actually began with a hypothesis, and instead the research was exploratory.
So I don't think there's a direct causal connection, and in fact it could also be said that results from social sciences have influenced the political climate in turn, though the education system. It's clearly a dialectical relationship.
Harvard may be academia, but I got the impression you were talking about people being ejected not for coming out with a paper that challenges the orthodoxies of social justice (of which there are many, just yesterday I read part of a PhD which argued that many forms of hate speech should not be restricted in a liberal state) but rather something else outside of the academic process.
I can't say I'm very much in favour of liberalism in general, and I don't think that restrictions on some speech lead to tyranny as it's frequently alleged they would. One need not be a trusting citizen to hold this position, and I see no reason why the state (or an organization, of course) should not be very opinionated about what it allows and what it does not. The question "what if they start banning the kind of things you say?" is a moot point when I'm not arguing for such a ban. Just as any restriction on speech might be uncomfortable for you, only some are uncomfortable for me. You will protest when Harvard starts kicking people out for left-wing or right-wing views, but I'll only protest when they start kicking people out for left-wing views. I make no secret of this bias, and I think the obsession with being as abstract and neutral in general has taken a lot of force out of arguments for how we ought to run society.