No conservatives are still conservatives. They don’t need to embrace post-modernism to oppose what they perceive as a heretical religion.

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.