I am reminded of a secular saying I like a lot:

"The hardest thing in the world...To know how to do something, and to watch someone doing it wrong....and to say nothing"
(like making cookies the wrong way, for instance,,or a martini)

This can easily be shifted to apply to many people who are religious: they *know* they are right, and it is very hard for many of them to not use ANY opportunity to 'witness' and spread the joy.........but in mixed groups is is almost necessary to limit both the amount and 'flavor' of the songs sung so as not to seem to be preaching instead of just sharing good songs.

If someone were to sing a murder ballad, no one is likely to think you are advocating killing pregnant girlfriends, and if you sing "Year of Jubilo", no one is likely to think you are promoting slavery.....but ifall you sing is 'praise' songs, or gospel exhortations, it is not unreasonable to suspect 'motives'. It can be a fine line, but since there are churches where those who believe can share religious songs freely, it is a good idea to mix up 'public' songs with some non-religious music, lest it get overwhelming.

I am, in case you hadn't figgered it out, NON-religious, yet I will sing a gospel number, if it seems to fit the mood, because it expresses something about the history of my tradition and is connected to other, non-religious songs. (If you have never heard Helen Schneyer, who is Jewish, sing Christian gospel songs, you have missed something special!)...but she DOES sometimes give proper disclaimers when she has a mixed audience.