Dear Paul,
Greetings! Thank you for posting in Microsoft Community.
As per your description, you want to stop SharePoint pop up continually asking to share confidential information stored in keychain.
We'd like to help you, please let us cooperate and please don't worry, we can work together to narrow down and resolve the situation.
You may try following steps:
1.Open Keychain Access on your Mac, search for all keychains that are related to Office and SharePoint, deleted them.
2.Open the browser where you accessed SharePoint online resource, go to delete all cache and cookies.
3.Reboot Mac, then check if the pop up still appears.
If the issue still happens, we do understand the inconvenience caused and apologize for it.
Could you share a screenshot of the pop up? It will help us have a better understanding of the scenario, we will continue helping you troubleshoot the issue.
Thanks for your cooperation.
Happy new year! Hope you keep safe and healthy always.
Sincerely,
Tina | Microsoft Community Moderator