Right. I have an ex-right wing evangelical now left-Democrat friend who tells me that she initially got hooked into a right-wing church cause they were the best show in town.
And you know that might be doable. A left-wing group could put on "the best show in town" on a weekly basis someplace even with the comparatively minor resources available to most left-wing groups. But the thing is, you have the broader rationalization in a church that you are not just seeing a show. You are worshipping God. Usually when lefties get together on a weekly basis it is for meetings. And no freakin way a meeting will be the "best show in town" or is even likely to be fun. I guess you could make it a weekly celebration or something. The "low religious content" services actually manage to pack a fair amount of ideology into them. No reason a weekly left wing service could not do the same. Do it in the spirit of "another world is possible". "Enjoy a piece of the future every week". Tie it to "Food not Bombs" or similar left social services groups so that you offer a social service right away. Start the way small churches do. Rent a storefront full time, or a slightly larger space weekly. I don't know. Hard to visualize as something people would really do every week. I know with Churches, the C&W song often include stuff about how when they go to church "my butt and my back and my necktie hurt". It is not just a fun thing. That is the sweetener. It is also seen as a duty. Even with the "outer church" a lot of people go, when they'd rather be home sleeping late. With a left wing secular equivalent, what is the driver that makes you go when you'd rather sleep in?
The old Communist Party, before it was destroyed, had some of the social networking you are talking about. You had the freakin meetings, but you also had dances, social centers, picnics, barbecues. A lot of playwrights and musicians got their start with CP help. Orson Wells and John Houston got their initial audiences via the vast CP network. My Mom remembers that when she lived in LA, the local CP had a baseball team the played against the Democrats and Republicans. But the U.S. CP is long dead, in spite of its zombie still walking around.
And I know all the ways the CP sucked - ties to Moscow, lack of democracy, twisted ideology, extreme rigidity and inability to adapt. But the social network was real and powerful and often beautiful. A hell of lot of good people did a lot good things within the context of that party they could not have done on their own. We have drastically different times. Different times, different economic structure, different social structure, different technological structure. Still if you are looking for solutions, maybe you need to look back prior to the old New Left, and see if any of what the CP did in building that social network is replicable, without all baggage and bullshit.