I'm female. I do not believe in god. I'm bisexual.
I am exactly the sort of person left out of worship unless I pretend I'm someone I am not and don't reveal my true self. I'm a fraud if I want to fit in - these groups rarely simply accept me going there for the social aspect.
I did spend several years in an ELCA church pastored and co-pastored by a woman and by a gay man, who made a point every week of welcoming non-believers to the service. It nuanced my worldview a little bit. They were lovely people, but the congregation was definitely fighting upstream in wider Christian culture.
In my mind, the main secular benefit of church (for people who were not excluded) was access to ready-made community, reinforced by a regular meeting space and rituals (like singing) that help people bond and process major life transitions. I've been on the outside for about five years and haven't really found anything that fills that space, although I'm always interested to hear what others have found.
Years later, not much has changed. The anger has faded, particularly as I watch some of those old churches dying (although not without some degree of satisfaction, I'll admit).
BUT, I do agree that it's widely under-appreciated just how sophisticated a social technology the congregation is. And there's not, as far as I've found, a viable secular alternative. Take away shared conviction about the transcendent and you seem to lose some kind of binding agent, like baking without gluten.