How do I log-out (or reset) Microsoft's RMS / AIP [Azure Information Protection] identity on a Mac for Word, Excel, Powerpoint and Outlook?
After a too long search:
Go into the Mac's KeyChain and look for an Application Password called something like:
com.microsoft.office.rmscache

(Search for RMS.)

I deleted this record.
Quit Word.
Opened the protected file again.
Now I get the RMS/AIP login Window again and can user another account.

For the record, logging Word out normally or using Microsoft's remove-Office-license-from-Mac-pkg did not have the desired effect. Office's license account, Word's account (providing OneDrive etc.) and RMS/AIP's account are three separate entities.
In a simple world you have one account for all of them. In a more complicated set-up you can use the provided work-around to switch accounts.
(Fyi, an alternative: create an extra MacOS user account.)

Breadcrumbs I found:
https://social.technet.microsoft.com/wiki/contents/articles/17214.ad-rms-information-resetting-the-office-2011-for-mac-irm-client.aspx
https://social.technet.microsoft.com/Forums/en-US/030bba52-551b-4f31-8394-589b00418e22/azure-information-protection-on-mac