Ok, first off: I think that you (OP) already have got an answer to your "question" but I'll like to share some of my personal experiences anyway!

I'm not training for parkour yet since my body is not in the right condition, but when spring comes I hopefully have the body I need/want. When that time comes I'm not going to be embarassed when I train in public.
When I was younger and I got myself an alternative look, I used to get a LOT of comments/glares but you just have to ignore that because in the long run, that is who you are and if you feel embarassed for being yourself in public and people, who you are most likely never to meet again, give you weird looks then you need to get a grip of yourself. Go out there and do your thing!
Anyway, you should see that some of those "regular people" are really jealous of you since you can do all those things you do (even if you are failing sometimes) and they can't. Think of it that way and I hope you'll feel much better!