Yes, separation of church and state is a settled matter; no, it is NOT in the Constitution. I assume by this point you've read the text at least once or twice and saw the non-establishment clause, and that's great; it means we can't have a state religion, and we can't tell people how to practice religion. It does not mean we can't have religion in government, per se; it means a religious basis is not, in itself, a legitimate legislative one. That's not to say laws against murder and rape are unacceptable because they also happen to appear in most religious texts, or even because the primary motivation of the men who passed that legislation was a moral and in most cases deeply religious one. The laws are good and valid in themselves, precisely due to their operation in a larger than religious sphere. How well they serve that role is the real test of the law, and the Constitutional test here is that it do so without promoting or favoring one or more religions over one or more others.

Part of the religious objection today is the impression the First Amendment is being used in various ways to actively marginalize religious thought, and when that includes the government it is itself a serious First Amendment violation. There's a feeling, to put it in British terms, that we'll soon have an "Anti-Test Act" whereby politicians will have to renounce all religious opinion or be declared unfit for office. "Jacobin" has always had a pejorative connotation in America, even with men like Jefferson and Madison; the closest thing we had to a Robespierre sympathizer like Fox was Thomas Paine, whom the French almost executed for his trouble (and supposedly had a deathbed conversion.)

Essentially, they're making fun of her for bringing up a valid argument they long ago won, but they're disingenuously pretending the point itself is invalid and ignorant when they know very well that it's not.