If you didn't have a child, would you be willing to accept a partner who does have children? Would you consider those children your own if the relationship was serious? How involved in raising them would you be?
I am childfree, so the possibility of me dating someone with children is close to zero. I have gotten involved with a man with tweenagers, and it ended up a complete nightmare and a brutal moment of realization that I would never come first in his life—ever. I had emergency surgery, and he was basically MIA. His eldest kid had failed to study for a class all semester long, and he "had" to help the kid cram for an exam rather than tend to my needs. So ... that was that. I have a lot of childfree and childless single friends who have had the same experience with single parents, being put on the far back burner.
I wouldn't rule out dating and getting involved with someone with adult children, but it would depend on the type of relationship the man had with his kids. Of course I would want him to be interested in his kids' lives, but not overly-involved—if that makes any sense.
The relationship with your spouse is the most important one you'll ever have. This is the person who will take care of you as you age, and then enter the last days of life. So relationships can only thrive when two people put each other first, above all others. Some people, like my parents, are capable of doing this. Others aren't. That makes it really difficult to have an honest conversation with someone with adult children.
I'm in my late 60s, too old and set in my ways to have to deal with someone's else children in my home. My kids are grown, when I want a kiddie fix, I visit my adult children.