This is true everywhere. If I want to watch people as I walk through the parkinglot, I feel embarrassed. People get a perplexed look, or get nervous and walk away faster. Sometimes I'll wear sunglasses, and it's ok. People assume I'm looking away.
Why are people afraid of being noticed?
I know why women often assume that a compliment has a motive... I know when I was younger, I was so desparate for attention or acceptance or girlfriend, that the only time I could muster up a compliment through my shyness was when I was very attracted to someone. I was awkward. Hell, even now I am to some extent, even just with friends who I haven't had a night of all-open conversation with.
But you see, it still exists that if I were to make a point of complimenting an attractive woman, I'm an annoying guy. If a woman were to make the exact same compliment, then it's ok. If a lesbian or bisexual woman makes the same compliment, THAT is ok.
Well, that's not exactly fair. Yup, I get sexually attracted to people, but I also can just simply admire a person without having a sexual motive. Hell, even if it were someone who in other circumstances would want to date, I should still be able to appreciate their existance.
So sometimes, in new conversations, when possible without completely breaking the flow of conversation, I try to bring up that I have a wife and son and that they are very special to me. More often than not, this helps put people at ease.
When people are at ease, conversation is more fun. More topics are available, and less awkwardness is felt. It seems that one of the biggest killers of any interaction is awkwardness.
This doesn't change things with people who hate men because of things that happened to them in the past, and a variety of other sorts of awkward/hangup issues. The only ways around that are misrepresenting yourself.
In that, on the one hand, you have this separate set of friends who you can now enjoy, but on the other hand, you have to maintain that lie, because otherwise, to most people, misrepresenting one aspect of yourself means that every other part of you must also be false, and you're just another example of why [insert category here] sucks.