I'm glad I found this blog post because I have been going crazy trying to figure this issue out. Our CEO intermittently gets prompted to sign into google. He is using Outlook for Mac on the latest Macbook Pro 16". The microsoft update utility says that Outlook is on the latest version. He will sometimes get prompted multiple times back to back. I have tried all of the following to resolve:
Delete duplicate keychain entries for gmail and outlook
Delete and Re-add the account
Uninstall Office and reinstall
Change the IMAP and SMTP settings from *.gmail.com to *.googlemail.com
Finally, today, after finding this post, I locked the keychain and then unlocked it and then deleted and re-added the gmail account to outlook.
Hopefully this resolves the issue but if not , we have a real problem on our hands here.
I also use a Macbook Pro with outlook and connect it to my work gmail account and I do not have this issue. It would be great if Microsoft could provide a definite answer to this problem.