You’re mixing up a few different things here.
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social logins skip password since auth is handled by facebook, twitter, google, etc
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invites make password temporarily optional but you have to follow the invite link again to “log in” which I think we locked down so much that effectively doesn’t work any more. You’d need to submit a password reset via email to get in after that, which requires setting a password.
It’s a long story but invites are designed to get people in and replying ASAP with a minimum of fuss, but they are NOT intended to let people skip setting a password forever.