Pretty late, but this solved for me, so it's worth giving it a try:
Close your Minecraft launcher
Click start and search for "Xbox Console Companion" app
Open it, and it should give you a warning saying that there's a new Xbox app for that, but just ignore it and sign in with your Microsoft account
After doing so open the Minecraft launcher again and when you try to sign in you should be able to login into your account
I think that the problem might be with the new Xbox App, since logging into that one doesn't work
prplyoru
Pretty late, but this solved for me, so it's worth giving it a try:
Close your Minecraft launcher
Click start and search for "Xbox Console Companion" app
Open it, and it should give you a warning saying that there's a new Xbox app for that, but just ignore it and sign in with your Microsoft account
After doing so open the Minecraft launcher again and when you try to sign in you should be able to login into your account
I think that the problem might be with the new Xbox App, since logging into that one doesn't work