How Do You Handle Dating Insecure People?

We all have insecurities but some have much more than others. Sometimes someone you like turns out not to be looking for a partner, but a specific character to play out to make them feel secure in their own gender identity. You feel pressure to play that role. Did you ever come across dating people who are insecure? Do you run the other way, try to deal with the issue(s) or put up with it?