Why would this apply to romantic forays but not other types of social overture?

The fact that chatting to random people merely means you're willing to let anyone be one of your acquaintances

In general, being someone's acquaintance cannot be considered an exclusive group to begin with, so there was no exclusivity to be lost.

It seems like it(becoming known as a person who tries to chat up random people) would happen no matter what you actually talked about.

If you only rarely* make a sexual or romantic pass it is unlikely that people would view you in such a way. Especially if you approach people who are not of your preferred gender, etc..

*[when you find someone who is actually particularly attractive to you, after you've gotten to know them a bit]