Sounds like a really interesting assignment!

I think that the Exclusive Bretheren church is fairly strict but I really don't know much about them and I'm not even sure they let strangers into their meetings! (Note: Bretheren church are pretty mainstream and different to the Exclusive Bretheren).

I've been to a mosque service before and it was really challenging. The service was chanted in Hebrew/Arabic and the men and women had to sit in different areas wearing certain things.

Another idea that came to mind would be going to a gun club meeting or similar. For me that would really push the boundaries!