In my experience, most groups that have Christian hymns in their repertoire are closet Christians at least on average. Even in the choirs that sing strictly secular songs, believers are overrepresented just from selection effects, since they sing a lot more.

But yes, there are choirs that stick strictly to secular repertoire. There was a "red" choral revival in the 70s, and of course worker and patriotic choirs go a long way back. They got to have something that unites them besides the singing, though. In my town the main secular choirs are the opera choir, which is united by their love of opera and classical music, and the chamber choir, which is 90% doctors and nurses from the local hospital.

Library.

Libraries are often community based, can hold events and talks, are an assumed "no cost" place too. I've lived in cities where you can go and play music on their instruments, use 3d printers, computers, access training, hold community groups, use their sewing machines, watch performances and more.

What you need is the funding.

I see what you are saying, but library isn't it. It needs to be an organization like a church, just non-religious. Libraries and churches have some similarities, but the many differences, and not just religious versus non-religious.

I want to see a purely voluntary organization. There is a head of the organization, but that person has a normal full time job, as does everyone else who "works" there. People need to pay dues to pay for the building, the utilities, the pipe organ, etc. but none of that money can go to a person's salary. No mega "churches".