As a non-American, I don’t think I‘m understanding the phrase gay “community”

First of all:

• Not trying to be controversial or divisive.
• If you don’t like where this post is going, please don’t hate. Just trying to educate myself on other people’s understanding of the phrase here.

What does “community” mean? My English is fairly good, so I don’t mean it in a literal sense. Rather, why do people (gay or not) just assume that because one is gay, he or she is part of a community?

I differ from most of my gay peers, lifestyle wise, politically etc. and it’d be false to suggest that we share many common interests that I don’t already share with other groups of people (the right to be unharmed, equality and so on).