Yes. Though you can do it yourself, a lot of furries go to conventions, frequent social media forums and bulletin boards. Just like you would with any other hobby or lifestyle.

is this a sexual thing

Sometimes but not always. The sexual part is a subculture that is part of the larger furry culture.

I don't know if there's any statistics on how large that subculture is either in raw numbers or percentage of all furries, but as an outsider who's picked up info here and there, my guesstimate would be that it's probably a small minority 🤷

Is it an American thing?

Already answered by someone else, but may as well include it here: nope. It's a worldwide thing.

Being openly a furry is probably much more prevalent in culturally liberal (in the original sense of the word rather than the political one) countries than ones that strictly enforce specific cultural norms. And Japan, probably 🤷