Participation in church-like, non religious organisations used to be more common.

That's kind of what freemasons, lions club, rotary and such are/were kind of like that. Social clubs. Unions sometimes played that kind of a role. Union meetings, barbeques, bars. Even personal identities tied into union memberships. A lot of organisations with names like "X society of Y" were actually "societies" at one point.

We are just far less affiliated than we used to be. Less church membership, probably less gang membership, social club affiliation, etc.

Some propose that those kind of clubs exist because of Christianity.

Paul told people to treat their wives like they were the Church, which lead to the end of tribes, the replacement of those large social/family groups with a more varied interest based group structure, which lead to more intermixing of ideas, the industrial revolution, and Western thought processes.

You might consider the Unitarian Universalists. They welcome everybody, including atheists, and they're pretty good people. I mean, people are people everywhere, but I don't think you'll find the same kind of problems that you find with other faith groups.

You might consider checking out Sunday Assembly[1].

[1] https://sundayassembly.online/about-sunday-assembly/