I am also strongly in favor of option 3. I’m building a community where people may reflect more deeply on emotions and I think adding that extra level of gating on the anonymous invite links (because they’re not tied to an email address or identity) could make me feel more at ease that only the people I want to join will do so.
I suppose I could make sure to use the invite email instead of anonymous invite link, but the link makes it so much easier to share in Whatsapp or other communication platforms.
So I’m also in favor of making the anonymous invite links respect the must approve users setting.
Also, I think if #3 happens, then the invite system can function almost as an application system for invite-only forums. Right now, I’m not sure how I would have people apply to be a member without having a separate Google Form or such. This could streamline it in a way, where custom user fields could be the application form—which is what I think @Wall-E is trying to do.