I'm going to ask my coworker if her children are adopted
Is there a problem if their kids are adopted?
I think so I am not pro adoption.
You shouldn't ask coworkers personal questions like that. Asking them these types of questions can get them upset at you.
I think it's okay to ask. They have to share their life stories with us if we ask, so I don't see why it's so bad.
If you are already implying adoption is a bad thing you really should mind your own business. If you keep poking around you could be seen as a  harasser and wind up in HR.