Let's think about a couple more ways that you could go about obtaining a community in the US.
leisure: clubs, cafes, live music events, bars, gyms. proximity: neighborhood, induced parent communities from child communities. functional: PTAs, HOAs, coworkers, colleagues.
etc.
You mentioned gyms:
tl;dr: Karate dojos are a kind of gym with lots of community -- maybe too much!
Original post:
Gyms are an interesting one. Most are relatively anonymous, I think. But my (somewhere between first- and second- hand) experience of karate dojos was that they are very tight-knit, almost cultish (though not entirely in a bad way). People's SOs often joined, not really because they were interested in karate per-se, but because it was a way to spend more time together.
The hunt for the Third Place, especially among those that are “not 20” is very real and comparatively difficult.
I happen to have met a smallish group of people that I can start to grow as a community with that I actually want to, but this is a recent development and I’m grateful to the people that found me.