Reporting back.
Installed IE11 and:
* cookies must be allowed.
* whitelisting (trusted sites) did not work (live.com, visualstudio.com, microsoft etc/etc) somewhy. Only thing i found was that at least VS2013 had a bug where the sign in process actually mistakenly checked javascript access against the "internet zone" even though all the sites were in "trusted sites" zone - maybe it has not been fixed with VS2015?
* setting internet zone to high security (basically disabling everything) and specifically allowing javascript (active scripting)
Uninstalled IE (+restart even though it did not ask for it, just to be sure) and its security settings remained intact.
Had no problems registering / signing in after that. Yay!
I'm guessing by uninstalling ie's front end you've removed the javascript engine. After all, javascript is a user side facility not a backend facility ...
The frontend does very little (UI platform etc?) ... AFAIK, anything related to rendering an actual webpage is not considered to be part of it (the whole renderer is a separate embeddable component that is made basically inseparable from rest of the OS).
Comments from more knowledgeable dudes'n'dudettes welcome.