It's rude to assume someone else wants to go to your church, is into your sect of your religion, is into your religion or is religious at all. It's dangerous when you combine that with power structures from a work or other environment.
>it's rude to assume that someone else wants to go to your church
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 askers' perception may be that it's a safe question, but there are too many situations where the question is dangerous. Do you really want to have to identify as muslim or non-chrich goer when working and living in the Redstates? Do you really want to have to identify as non-religious when everyone around you is? Will your religion - or lack of - transmit your political leanings, which are opposite to the others around you?
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.
This may be a cultural thing, but inviting someone to go to church would be at least astonishing in France (and the rest of Europe). This is just not the place you go for a date.
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.
In some countries that still plays very badly and it could change your relationship forever.
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.
Ah I see. I guess location context is important. It seems odd to me as I live in NZ a very secular country, with little to no political implications of church attendance.
If anything I'd expect to get ridiculed for believing in something science couldn't prove.
I had a high school German teacher who said politics and religion were two taboos for polite American conversation, but Europeans can have more civilized discussion about these topics.