I understand what you're saying, and what you've said about. But this is largely a semantic question because "natural" has lots of meanings. I agree that civilization could be natural for us, but if our personhood as a whole is anomalous, that kind of naturalness or normality is still strange in the larger context. It's like saying, "It's natural or normal for a serial killer to evade the police." The serial killer would still be a deviant, though, relative to society.
I made the same point about the relativity of preposterousness, in the article below. The cognitive default shifted with the revolutions that Burke was living through. I'm aware there are late-modern reforms of mass irrationality, religiosity, hysteria, and so on. But I don't see how that saves Burke from the objections I presented in this article.
The main problem is the naturalistic or genetic fallacy. As a conservative, Burke is saying the religious traditions are good because they're old, so the older the better. That's fallacious even in Darwinian terms (because of the possibility of exaptation), and there's no independent justification of Christianity in Burke.