When I click on the Myibay icon, the little window opens as usual but sticks on "Processing" instead of offering the log-in dialog.

Tried reinstalling the addon; no help.

Mac OSX 10.11.6
Firefox 49.0

Please avoid sending the same question multiple times, it will not speed up the response.

Back to your issue:
It looks like you have some setting or add-on which prevents redirection.
You can try to disable all add-ons and enable one by one to see which one is causing it.