Check out the podcast from the Law & Liberty site. Here is Hamburger's book.
My brief thoughts:
I don't always agree with Professor Hamburger, but he's always worth reading.
One of the things that strikes me while listening to the podcast is what Hamburger refers to as "theological liberalism" has some meaningful connection with the concept of "primitive Christianity." And that term was invoked quite a bit during America's founding era.
A lot of academics and ordinary folks are under the misconception that 18th Cen. "theological liberalism" must mean something like strict deism. It's actually a much broader concept. The Unitarianism for instance of William Channing (who was an Arian) who Hamburger mentions in the podcast is a more typical theology.
Hamburger then notes much of theological liberalism defined itself in opposition to ecclesiastical authority, with the Roman Catholic Church being arguably the greatest "offender" against which to guard.
However, ecclesiastical, clerical and creedal orthodox Protestantism is also viewed with suspicion. High Church Anglicanism, which is Tory, is probably the 2nd biggest religious threat to the theological liberalism of the American founding.
But other kinds of Protestantism too would qualify. The idea of "primitive Christianity" is that Christianity was pure before an organized, ecclesiastical hierarchy took over and corrupted the faith sometime early on (like in the 4th Century).
Yes, Catholicism would be the main target. However it's not ONLY Catholicism; it's also many different kinds of Protestantism as well. Arguably it's all of orthodox creedal Protestantism that offends as well. This is why the theological liberals tended to like the Quakers, even if the liberals were Whigs and disagreed with the Quakers' refusal to take up arms.