Personally, I don't have any children. The last guy I dated didn't tell me he had children until 1 month after we dated. And sometimes, I'm afraid to ask a man if they have children because they will think that I'm judging them.

Children are an important issue, so simply ask. If he feels judged when you ask normally, it's his problem, not yours.
Maybe you are okay with a guy with kids, maybe not. Both are okay. But you'd need to know about him.

For me it's a deal-breaker. I'm 48, got to kids 24 & 21, I am not looking for another family situation. So if a guy has young kids at home, I'm not interested.

(Young) children define most of what a couple can do in a relationship, so rather important to know. I prefer to know before I even go out on a date. Don't want to waste my time, nor his.