I think it varies a lot by gym.

Ironically (for this thread), all the private rich-person gyms I've been to have mostly been populated by people who were not in good shape, and everybody was very friendly.

But these were also "health clubs" in the old school sense, not a fancy gym like Equinox where I would never even set foot.

Edit: I also have heard enough gym bullying stories to believe that it can and does happen, but it seems maybe only under circumstances that I have never been in.