I tried all the typical "delete your cookies" solutions - nothing worked. Ultimately changing the user's admin roles worked for me.
Here's what I did:
- Log in to https://admin.microsoft.com/ admin panel with any other user
- Click on Users / Active users in the sidebar
- Select the user from the list and then click Manage roles
- Select only the relevant roles here. If the user is an administrator, then unselect everything and only select Global Administrator
As I understand the issue is that if you have several overlapping roles the system tries to log the user out and back in with different roles, causing an infinite redirect loop.