Can't say this is a problem that has ever reared its head in my experience. The nearest I can recall, is when a well intentioned minister tried to insist that the fact that someone had been singing a hymn with such power and evident conviction had to mean that, deep inside, she was a believer, and she objected most strongly.

Mind, that was a good song. It's not something that would arise with the kind of "Praise Song" that I think is envisaged here.

But I don't believe in the idea that just because a religious song isn't "inclusive" it oughtn't to be sung outside the particular religious tradition from which it comes. I value the chance to hear songs from other traditions. The crucial thing is they should be good songs, and they shouldn't be sectarian in the sense of being disrespectful of others.