Humanism?
Quakers?
The best local churches are the ones that buck the system. We had a catholic church in South Brisbane where the priest, Peter Kennedy, just went his own way, welcoming everyone whatever their history, sexual orientation, lifestyle etc. He did loads of social work, helping the homeless, providing food and such like. Here's a precis of the story by wikipedia:
en.wikipedia.org/wiki/Peter_Kennedy_(priest)
and a more in depth report here:
stmaryssouthbrisbane.com/2012/08/troublesome-priest/
He got booted out of his parish, but the Labour Party gave him free use of one large meeting room in their party building, and his parish grew from there.
The official St Mary's church plods on with a small traditional congregation.