Oh yeah, our school is exactly like this. you have to know someone to be able to participate.
when my DS 10 was in first grade I got a message on my answering machine that went like this: Hi Mrs. --- your turn has come up to participate at school. The Thanksgiving feast is next week. I see here that you work full time. We have lots of moms who would like the opportunity to attend the event, but it is your turn. So, if you can't make it because of work there are lots of moms to take your turn. If I don't hear from you today, I'll give your turn away.
So I call the woman back & tell her I wouldn't miss the opportunity. What about work , she asks? Well, they do let us have a few hours off per year.
Now every Thursday I have a standing meeting with my boss and a few others. I called him & said re-schedule the meeting. I'll come early, stay late but I'm going to the first grade TG feast come He-- or high water.
I get to the feast & this same woman comes up to me and says, we have too many moms here, you can leave

I looked her square in the eye and said tell one of the other moms they can leave. I'm staying.