How to prevent people from adding other people in an iMessage group? Is there some setting / block / third party app where I can prevent someone adding another person to group messages?
In short, no, it cannot be done.

No-one "owns" an iMessage group, it's entirely ad-hoc - so who would be the moderator of who can &amp; cannot be in it?

What you can do is leave the room when you are invited or turn on do not disturb for a noisy room if you keep being added by “helpful” “friends”.