I’ve met people like that, I think those against abortion are more common and their reasoning is that the child is alive from conception or the moment its heart starts beating, and it deserves human rights from that moment. This idea is independent from any belief in god.
Same goes for homosexuality, personally I think it’s because some men (I’ve never met a non religious homophobic woman) find their own sense of masculinity or sexual identity challenged. I’ve never met a young person like this, all the examples I can think are from people who should be at least 50 yrs old today.
And honestly? I think it’s more of a cultural thing. I think I’ve met these types of people just as much as I’ve met backwardly religious types. In some countries you have a lot of religious thinking but not in others.