Now I know why you're asking I have to say no, I can't think of any natural term people already know that doesn't distinguish their own religious buildings from those of others. I find this totally natural because my undestanding of religion is that it's a method for forming a communal identity, so "our space" would be the word's function: a sense of other people's truths as potentially equivalent to our own strikes me as a pretty new phenomenon that could only develop after different bases for identity (eg nationalism) had become well established.

That anonymous comment above is me, BTW.