I've tested it a few times myself now. New registrations are sent into a direct loop after they submit their registration information. Any attempts to visit the site while the site recognizes me results in the direct loop error message.
As described in a previous support ticket-https://premium.wpmudev.org/forums/topic/im-getting-a-redirect-loop-when-logging-in-as-a-registered-user
by ascribing that user a new access level (essentially the same as the guest access level) they are able to use the newly registered user without going into a loop and select a subscriptions.
I think in the time between registering and setting up a subscription, the user is losing all access (including to the restricted access page) and it is stuck redirecting itself.
How do I fix this?