You might want to check out the Unitarian Universalists, they provide many of the social benefits of organized religion without a specific belief system attached.
UUs have seven principles (https://www.uua.org/beliefs/what-we-believe/principles) but none of them require any sort of supernatural belief. Coming from an anti-theist background they were all already things I agreed with. Some people say that you can believe in anything and be a UU, which isn't quite true - any belief system that sees others as "less than", for example, would be incompatible.
As for who does the talking, most congregations have a trained minister (like my partner) who leads most services. They talk on a variety of topics, but mostly about community, justice, activism, and lessons from other religions.
Hope this helps!
My impression was always that UUs were a sort of offshoot of Protestantism; I think "Unitarian" refers to their non-belief in a trinity of beings that are a core doctrine of most modern Christian denominations - is that right? Would you say that UUs have entirely abandoned their Christian / Protestant heritage other than the form of the service?