Recently I was looking around on Facebook as you do, and I realized that around 90% of my news feed was full of "John Doe joined the group ... and so did 16 other friends". Now apart from the annoyance this served me it made me think about the purpose behind such groups. One could argue that they are simply the musings and observations of a random person, but I take a more cynical approach. Why? Well I can understand why you might want to protest against racism by joining a group to show your support; but what possible reason could there be for joining a group just to agree with a meaningless statement such as "I want this house" with a photo of a large house? Sure for most people it is just a small thing they do when they are bored. But what worries me is the people behind the groups.
Think about it. If you were to take a handful of groups and add together their memberships to say 1,000,000 people, you would have a good amount of people to spam. If you wanted to spam a certain set of people, you could take student groups and collectively spam them. I can see large shady businesses buying "admin-ships" from the creators of these groups, as to utilize the "Message all members" feature of the groups system. And think about it, this wouldn't just impact your Facebook account, no, because Facebook is automatically configured to email users whenever they are sent a message, and so it would filter down.
Now you might be thinking, yes but all these people could just leave the group. Sure they could. But if the attacks were well coordinated, you could send maybe 10 messages to every account you had access to in a minute? And that's the sort of thing that wouldn't even require a bot network. You could just copy and paste in the spam over and over. You would segment the attacks into a group by group basis and make sure you were targeting the right people.
I would advise you take this idea with a pinch of salt, because I can't see it happening in the near future, but I think it is important for us to be aware that such a network could easily be used to spam people. So what can you do to stop it? Don't join these stupid groups that say "If 250,000 people join I'll run round town naked", only join the ones that mean something to you and that you trust.