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I don’t think Lemmy has it (there is an open issue for invitation links that I don’t believe anyone has worked on). I don’t think MBin or Piefed have it either. Not sure about Mastodon. The beauty of FOSS though is if someone wants it bad enough, they can implement it themselves.
This is the most important thing here. Additional thing to consider that in my experience devs regularly overlook: how easy is it to implement and support?