at least the US has a pretense of keeping the church out of things while it infiltrates all corners
What you need to understand about the UK is that we live in a theocratic monarchy that we've jailbroken and installed a representative democracy emulator on.
A lot of the UK governmental systems are things like "officially the king gets to choose the PM, but in practice he will always choose the person parliament tells him to choose". Nobody really knows what would happen if he didn't, but my guess is we'd all just ignore him. The church has official power, sure, but generally speaking they know better than to actual try to wield it. If a politician starts talking about their faith as a motivator for their politics people think it's icky.
America is what happens when a bunch of philosophy bros look at a messy, real world system that seems silly but broadly works and decide they can do better. It's a VC startup. It looks great on paper but how many industries are actually healthier after they're done "disrupting" the indigenous population status quo?
