Go look at these arguments about confederate statues. Liberals condemn the moral faults of the person. Conservatives excuse it as values of the time; moreover they appeal to the virtue the society has chosen for the statue to represent. There’s nothing more post modern than that.
From your post, it seems your view is that conservatives adopted these tools because they are the tools of an oppressed minority, which conservatives now perceive themselves to be. I think that very well might be the right explanation. But I also wonder if this shift is more of a demographics thing. Post modernism can’t be the young, hip mindset for the rest of human history. I wonder if young people today are carving out some new view of the world, which is far more interesting to me than arguments over celebrity Twitter accounts.
Insofar as right-wing people now invoke the liberal notions of free expression it’s only because that was a middle ground that allowed coexistence and liberals are now sitting aside while progressives try to blow up that compromise. (And also because a bunch of center right people think it’s a good thing—it’s not like the right is uniformly absolutist evangelical types).
Put differently, Christian evangelical are angry that liberals broke all these taboos in the name of free expression, and now progressives are trying to treat Christian evangelical beliefs as the basis for cancellation. There is nothing hypocritical or contradictory about this.