You're not assuming anything, you're asking them if they want to come. They can always just say no. Not everything has to be the end of the world. Of course you could make up tons of situations where this could be inappropriate (I heard you had a drinking problem, would you like to try church instead?) but I think in general it's a safe question.
The invitation to a (particular) church can come across as part of a package of high pressure to conform to the rest of the team. I've received these invitations while living in the US, and yes, it was very uncomfortable.
If the invitation is from someone in power over the receiver then it may be received/perceived as an order.
If only there were a way you didn't have to assume, but could find out...
There could be some circumstances where this is possible ("hey, my church has its annual fiesta, plenty of people dressed up in a traditional way - you know, the famous one! Wanna come see that?", or a marriage/baptem/other family / friends gathering) but this is not the first place which come to mind when thinking about dates.
Co-worker "What did you get up to this weekend".
Me "Just the usual. Lazy Saturday, church took up most of Sunday, what about you".
Co-worker "Not much just watched a few movies. You go to church? Really?"
Me "Haha yeah I do, you're welcome to check it out if your interested."
is something you will never hear from civilized people in France, not in that context.
People will discuss religion as part of a general discussion, but context is everything.
In the USA, which is an extraordinarily religious country versus other Western countries, the response is likely to be more nuanced, but there are sill the many matters of which religion, sect and so on to consider. Going to a (particular type) of church risks being seen as a political statement as well. Best to avoid.
If anything I'd expect to get ridiculed for believing in something science couldn't prove.
Is this not true?
Politics yes, and I would not say that it is very civilized, so people avoid it not because of political correctness (so to speak) but rather because these discussions tend to get heated.
Otherwise, yeah, but I think it matters a lot what crowd you hang out with. The USA is a big place, and so is Europe.