First off, as I noted in an update based on a comment from Radjah Shelduck, Jefferson wasn’t referring to the Catholic Church with “pernicious Rome,” but to the Roman Empire. That’s not to say that Jefferson was particularly friendly to the Catholic Church, but its influence in the colonies and US was minimal in Jefferson’s time, and for decades afterward.
Even with that aside, using Jefferson as an argument for federal intervention in just about anything reveals a much deeper ignorance of Jefferson, the political winds of the era, and which side of the political divide Jefferson ended up representing. (…)
In fact, we have a historical record for Jefferson’s thoughts on the freedom of religious expression specifically for Catholic nuns, in his own hand.