There are always going to be some things that people believe we shouldn't be able to decide, even for ourselves. Someone else on the thread posted about consensual cannibalism -- most people would consider that over their line. A lot of it comes down to whether you believe we (as gotsa said) "fully own ourselves" or not.

Note that religious believers don't "mix" God in their arguments, they're just speaking from their perspective. They believe that God is just there, that he made and guides everything. What you call "mixing God in" we might call "practising what we preach". It's maybe a bit like asking a Native American to stop "mixing their tribal culture into everything". That's just who they are.