I'm a pretty outspoken antitheist, so it would probably be a
little awkward if they identified as religious. I can bite my tongue with people all up the spectrum until they reach that "holier than thou, won't shut up about church" kind

So yeah, if the guy is religious to the degree that is common where I live (vaguely so, usually moderate and has a loose interpretation of their religious texts) like my family members and some friends, we can absolutely date/marry/whatever.
Raising kids would be tricky however, as I detest people who indoctrinate their kids with their religious beliefs. It can be presented as an option as long as they are educated on all the arguments for/against, but to simply force them into houses of worship and reading whichever religious text "x" amount of times a week? That could be a deal breaker.