Society cares, that’s the point. Society cares about who you have sex with, and society cares about whether something is genetic. If society didn’t care we’d be having a different discussion.
Clearly there are multiple societies, with varying cultural norms (as we can see from the range of opinions here). While you can't have societies without individuals obviously, you can only barely have individual humans without societies (and they're usually not doing too well, a few hermits and mystics notwithstanding).
Society cares, that’s the point. Society cares about who you have sex with, and society cares about whether something is genetic. If society didn’t care we’d be having a different discussion.