XF 2.1 Weird issues with Xenforo forms, password dialog

Since we upgraded from XF 1.5 to 2.1, I get the feeling something is off with our forum installation. In this instance I have identified a very simple functionality that is broken. If I try to enable 2FA, there is a password confirmation prompt before you can move forward, exactly as you see here:

In this page in my forum, if I enter a wrong password, I get an overlay indicating so.
However if I enter the correct password the page simply refreshes, with an empty password field.

What could be the culprit here?
I have tried it with different browsers and no add-ons. Same result.

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PS: I recently reported some issues with registration since the upgrade. That isn't fully resolved yet, we had to disable social logins and leave the most bare registration possible which seems to work for most users. Still, something is definitely off.
 
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