Well, then, you said it very oddly by only mentioning the one way as if it were the whole issue. But then you still run into the problem that way is largely hypothetical; as I said, there doesn’t seem to be any good indication that rejection of evolution has actually grown in in response to vocal criticism of religion.
That happens a lot across the board, sure, but there are also problems with denying funding needing for research, muzzling scientists, and even mocking the basic idea of research.
For instance there’s a special contempt you saw when Palin was out ridiculing the idea of studying flies, as if our whole conception of genetics and developmental biology didn’t come from that. That was her playing to some group of supporters, and I don’t recall anything similar in the other party; but let me be unusually fair and say it’s possible I missed something.
The muzzling of research, though, seems to have been something peculiarly high to the Bush administration. There are lots of normally politically-quiet scientists who complained of it, especially in fields like climate science. The opposite case - let’s say GMO research being stifled, or something like that - does not seem to have happened before or since.
People like to say so, and it’s probably true if you’re talking about people who aren’t in power. But if you are talking about them, well, some of us were paying attention when a Democratic president passed a primarily Republican-based health care plan as a compromise, and the other party shut down the government over it. Nor is that an isolated example.