For example: In work and social life, I’ll give my phone number away to people I meet. But I’m not interested in relationships, so I’m far less likely to give it to women, since I don’t want to give anyone the impression I’m making romantic advances by doing that.

As someone who is relatively active in volunteering/local politics, I've been thinking about printing up some old-fashioned "calling cards" (like business cards, but not for a business). Maybe you could do the same, and seeing that giving out your contact info was such a routine habit of yours that you had a ready-made solution for it would stop women from getting the impression that you were leading them on?

...then again, maybe not. Hmm.