Today I wasted about 4h to figure out why I couldn't login to https://outlook.office.com respective https://outlook.office365.com nor I was able to connect to https://outlook.office365.com/ecp or its new version https://admin.exchange.microsoft.com/.
The ladder both at least did let me in from time to time - browser and computer independent.. .even on Linux I was rejected or not... absolutely erratic. Same with the user experience URIs, which did work - same browsers as with my Windows device - at least under Linux.
I tried much of the things, the web was willing to offer by searching it and was close to give up. I even did turn off all security measurements and started the good old Wireshark but nothing really led me to the solution - which I will not further keep away from you :)
When I did setup O365 I was not happy by just adding some roles to my account, I just added all roles - why not, for setup I didn't want to fall short nor wanted to be the Global Administrator before establishing MFA.
I than found
at Microsoft Answers: Repeating redirects detected. Scroll down, I here cited the last answer above already, however, you might want to thank Anna Ma MSFT for this solution, if this helps you to overcome the here described issue - I did so and herewith again:
Thank you Anna Ma MSFT.
Despite the fact that Microsoft Exchange Online Team might want to expand the error message to e.g. "Cookie not found" or something like that and not the five or six different, misleading error messages, I again found a point speaking against Cookies - modern browsers do deliver alternative solutions; and here I don't need to write about GDPR compliance or related stuff.