If you want to be coherent with your logic, you have either to hear what the Nazi leaders said as you're listening to the founders, or you have to consider in which religion they were born in, like you do for the Nazi leaders.
John Adams: born in a congregationalist (puritan) environnement. Did embrace Deism or some form of theistic rationalism
Benjamin Franklin: bron from a Puritan family. Did embrace Deism or some form of theistic rationalism
Alexander Hamilton: was Presbyterian earlier in his age, then Episcopal. Did embrace Deism or some form of theistic rationalism
John Jay: was Episcopal
Thomas Jefferson: was Episcopal. Did embrace Deism or some form of theistic rationalism
James Madison: Presbyterian. Did embrace Deism or some form of theistic rationalism
George Washington: Anglican family. Did embrace Deism or some form of theistic rationalism
Not one wasn't born in a protestant environnement. Even if most embraced some form of mixed Deism or theistic rationalism. You have here a classic freemason and liberal influenced and influencer bunch of people, at the times where freemasonry was at its peak of popularity and on the raise, as well as at the time of the birth of liberalism.
And by the way, the separation of the church was an idea that Martin Luther had. John Locke advocated too for the separation of the church, and was also a protestant, he's the one who justified the theft of the territory of american Indians. He definitely heavily influenced what happened in this continent until the creation of the United States. I mean, he's one of the founder of liberalism, the ideology of the United States.
So we have a clear continuity with protestant and anglican christianity and the ideas of the founders, and that without a big rupture, as much as we would like to see modernity as an era of ruptures, most of the times it's actually a continuation of past ideologies and religions. Nazism, as well as liberalism, were in continuity with the past, this doesn't mean, we had to get throught this the way we did, we could have well seen the nazi party being smashed if the liberals weren't scared by communism and hadn't seen Hitler as a rampart against communism. And now the future lies past liberalism, and on and on. So history goes.
For example the European Union is heavily influenced by catholicism, more than protestantism, which kinda explain, more or less, the Brexit. It's always more complicated than that, but people and political institutions are predictable none the less.
The rise of Nazism seems, as most far-right movement, to hold back to some highly disconnected ideas in the sense that their history is short with a lot of discontinuation between all of them. They're opportunists, take whatever they have to be granted power, they're oftenpseudo-revisionist (as revisionism is something historians do, but with sources and methodology), so they build a new history out of fabricated pseudo-historical sources. They're a product of modernity and if we have to consider a political movement which really want to make ruptures, it will be the far-right movements. We can now make a history of those political movement, not so much by the direct content of their thoughts, but by the way they address the present, the future and the past. The past being glorified and the present being decadent, the future being the rebirth of the past, an idealised mythical past.
To build a bridge from Nazism to catholicism or even christianity is to forget that religion could be a tool as much as anything else for them. But at the same time, catholicism is clearly more compatible with nazism than protestantism. The content of Nazism doesn't hold so much idea of catholicism quite the contrary, it's mostly a rejection of communism and international free market capitalism and a rebirth of antiquity, christianity is rarely mentioned. The content isn't really there, or when there's one, you'll find two paragraph later a contradiction, but they don't care so much about contradictions. What's important is to speak to the emotions of the public and to constantly engage in conflictual interactions so it seems that there're no reason to be held, just "we win or we lose", but if we can include most of the people in the "we" through emotions, then everyone think in terms of us against them and so the far-right party can rise to power.
Far-right movements are auto-destructive and most of the time they don't last long, but more your political ground is closer to the far-right, more you keep a door open to them, whatever is the content of your thought, if your political agenda is to keep things like they are or to come back to a glorified past, you're transforming your public into a prey for the far-right.
And something else, which have been often missed, is that the idea to create an historical rupture, is also condemned to create a reactionary movement. If your political agenda is meant to create a whole new order in deny of the historicity of the social movements which cross the society itself, you get as much Nazism than Stalinism or Maoism. It's not to say we shouldn't think about the future, quite the contrary, we have to get past liberalism once and for all, but we need to do it with history in mind, liberal ecology is as stupid as primitivism, we need post-capitalist ecology, we need a post-modern ecology while acknowledging modernity and all the ideologies which structured modernity, from liberalism to marxism.
I'm anarcho-communist by the way, so I'm not advocating for middle ground, just so you know. But I kept my comment out of the subjectivity of my political position. I almost never advocate my political position, I prefer to take a critical stance whenever I can.