I have looked at the Bungie Help Twitter and seen that the issue is still not solved.
But I'm here because they also said for anyone experiencing the issue to report it here.
So here I am.
Just logged in this morning and gotten the message telling me I have no permission to access the Mulitplayer Gameplay or someone else has logged onto my profile.
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You may want to try running through these steps as it has solved this issue for other players: (1) Log out off your PS4™ console (the account that's having the connection issue). (2) Power down (turn off) your PS4™ console. (3) Go to PlayStation.com via a web browser from your PC or Mac. If you are currently signed in, you must sign out and then sign back in. Confirm you are are signed in. Then log out. (3a) From Mobile devices using a web browser For Apple: hold down the refresh button on the URL and click on “Request Desktop Site." For Android: click on the 3 dots on the top right corner click on “Desktop Site." (4) Login and out a second time. Confirm you are are signed in. Then log out. (5) Go to your PS4™ console, turn it on, and login.