At non-religious schools, kids won't be singing hymns. So that's not really applicable.

My own kid goes to a C of E primary - it's the local school - and does sing songs about God and Jesus. I'd prefer it if he didn't. But we talk to him about it, make it clear that it's not something we believe in and that we regard them as just stories and songs. I regard them as much less problematic than language about 'strong Britain' and enduring wars - the religious songs he gets at school is mostly modern stuff that isn't even especially patriarchal and is mostly about being nice to people.

That there are songs sung at school we don't like doesn't mean we should therefore welcome more songs at school we don't like.