They're all different! If it's a requirement that you help out, I'm sure it will be made clear to you early on. Some small co-operative type groups do want everybody to take a turn in running the group or organising activities; there will be a rota and your duties will be specified. Other groups are run by whichever people want to be involved, recognising that not everybody wants to or is in a position to do that.
I attend groups in which I never ever help out, other than maybe washing up the odd teacup. I go to one in which I do sign up to the volunteers' rota, but rather less than my fair share. I run a group, in which I don't expect significant help, except I may approach one of the most regular attenders and say, "I'm on holiday next week; would you be willing to run it so it can carry on without me?" And I'm very grateful whenever one of the other parents helps keep my younger child from getting bored and disruptive, which frees me up to run the session. I've organised a few one-offs and not wanted any help... I'm somewhat commitment-shy, and so I prefer doing one-offs rather than "signing up" to do anything on a regular basis.
"From each according to his ability, to each according to his need", I reckon. Some families just can't contribute as much as others, at least not at a certain phase of their lives. Their time may come later. Those of us who are able to help may still be able to pick and choose our roles, contributing in the way which suits us and leaving others to pick up the slack if they are happy to do so.