I don't know, I don't have insecurities relating to personal identity (despite being in various categories that some people would label marginalized, though I disagree with that worldview fundamentally) so I can't say how people who do have such insecurities think. If I joined a group about XYZ it would be because I want to engage in XYZ activity or discuss XYZ topic with others, just like religious people go to their various religious activities and so on. I'm not disagreeing that some of these people in Mensa, parades, etc may in fact feel insecure, but I do want to point out that engaging in a group about a topic doesn't mean you're insecure

People like celebrating their roots even if they don't feel insecure.

Overcoming shame is part of gay pride. But it was also a way to overcome marginalization. And lots of people go just to have fun now.