Singing along to songs that have a background in another religion

I recently met with some folks for singing circles, where you just meet up and sing together for the fun of it, as a low-barrier setting for those who feel they can’t sing, but want to. It’s an inclusive setting. Usually, there also are some mantras that are easy for everyone. However, now that I’ve had a closer look at the meaning of some texts, some of them basically praise Shiva as g-d or address Kali, which are Hindu deities.

I’m converting and it just feels wrong “to my soul” to join in to these specific songs, so I won’t do that anymore now that I know the meanings. There are borderline cases (seeing similar texts more through a historical lense or just singing about “mother nature” for example), but straight up praise to Shiva I can’t do, as for me the oneness of g-d is central to my own beliefs.

To be honest, I know that those in this group are just a bit hippie and don’t see the religious significance in these texts – they see it as areligious, just something to sing together in a secular setting, easy songs for everyone to join in. I like those people, they are super nice and always make a point to be inclusive, so I would like to address with them that such texts, while they might not have issues with them, can indeed act excluding for those of other faiths. I feel like as an atheist, you can just sing it, not taking it seriously, so maybe they assume this is the default mindset for everyone.

I have had similar experiences where some Christian songs are cultural campfire classics, just sung by default, without any second thought and now that I look back at it, a large part of “social” songs are influenced by at least Christianity.

This led me to the question, what are your experiences with not religiously neutral songs and similar? Would you personally sing along to something like this in a social setting, and if so, where do you draw your line? Are you able (and willing) to just see it as something that is not meaningful if you do it without intention, or is performing the act already crossing a line for you?

(Interested in your personal opinions on this, especially as here are so many users of different denominations)

Shabbat Shalom!