Each Friday evening for the last few years I have had a song circle at my home. 12 to 20 people show up, with a core group of 10 or so. (On occasion, someone will bring along someone in town on tour and we get to hear some really neat stuff.)
As said by someone above, the selections go 'round the circle- or you can pass, or you can request someone else to do a tune or song (that doesn't count as the other person's turn). There aren't many restrictions- except it's all acoustic, no drums, no Beatles. (!) {I also don't like 'Cluck, Old Hen'. So there.}
A typical evening consists of fiddle tunes where everyone plays fast and furiously, with the songwriter types participating by watching others' chords; original songs (everyone backs off and makes sure we all can hear); a young lesbian couple who sing very well together (and one of whom has a remarkable voice) do a lot of Indigo Girls; one man with the warmest voice you ever heard does a lot of Steve Goodman/John Prine/Shel Silverstein/Randy Newman/Jesse Winchester; one man who has a tenor voice and a tremendous memory for lyrics does a lot of folk songs like 'The Colonial Boy', 'Across the Great Divide', 'Ramblin' Boy', 'The Escape of Old John Web' and the old version of 'Wildwood Flower'; one man who has a great voice and a wondrous memory does old country songs, none younger than the 60s, (He does a lot of Webb Pierce, Ernest Tubb, Faron Young, Lefty Frizzell, you get the picture); one of us does a lot of Carter Family and Ginny Hawker; another does songs like 'Monongahela Sal', 'I Never Will Marry', 'The Texas River Song', etc... Of course, we all sing along on choruses and whenever and wherever the singer wants harmonies.
Instruments range from fiddle, mando, banjo, autoharp, guitar, harmonica and back again. And voice. Lots of voice.
My point is that we bring a lot of different interests and approaches to the table, and we all contribute, we're all welcome.
It may take time to find/create a group like ours but it can be done. As I told one friend who had recently moved to a village: If I move to a town of 1000 people, I know there are at least 30 people there who play something; out of those 30 there are at least 10 who would like to play with someone else; I'm going to find those 10 people.