I think you're talking about two different things here.

One is the "supportive positive social groups are beneficial, and church is the only one around"

and the other is "atheists are a grumpy lot but religious people are all happier from their religion"

I won't comment on the latter for now.

I can, however, attest that it is perfectly possible to find non-religious supportive social groups. Not just self-help groups - and I really think you should rethink your idea of stigma... a "single parents" group or an "ethnic expats" group has (or should have) zero stigma attached. There are also many other socially supportive groups.

I, personally, am not only a geek, but also a bit of a nerd. I belong to a group called the Society for Creative Anachronism. We're a bunch of people that use "medieval recreation" as an excuse for dressing up nice, eating feasts and learning ancient forms of crafts and/or sport. It's a hell of a lot of fun... it's also quite a thriving community. Totally non-religious.

With the principles of "Honour, chivalry, and service" it's also got its own morality...while I personally have never done a midnight rent-donation, I have seen more acts of effective charity than I ever did when I used to go to church (mainly because I don't consider evangelism to be a form of charity). We're a world-wide organisation and I recall the outpourings of help for friends and strangers in time of need (eg the Katrina victims), as well as locally (eg for the Aussie victims of recent natural catastrophes), but mostly for acts of individual, personal service.

I've personally seen countless personal acts of altruism of this sort. A lot of our events are outdoor camping events, run entirely by volunteers almost universally for zero profit (the few for-profit events I've seen were basically fund-raising for some other event for the group). But even the non-organisers generally help out too. From manning the registration desk to heading out back to the kitchen to wash-up. From helping a burdened woman carry a heavy load, to helping a newbie pattern a frock or build a helmet, or all pitching in to help raise somebody else's communal tent. I can't remember the number of times I've seen people give away their stuff to newbies to help them get started - with the general advice going with it of "just do this for somebody else some time".

I am constantly surprised at how well this philosophy works on bringing up honest, sharing children that actually help each other without being asked... (proof that it doesn't take fear- of hell to motivate ethics if ever I saw one).

So yes, it is possible to be part of a completely non-religious social support group.