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When Microsoft transitioned to a Chromium-based browser they become somewhat less motivated to support non-Chromium platforms, and when Microsoft released a new version of Skype for the Web in 2019 it only supported Edge, Chrome and Opera, and did not support Safari or Firefox.
Microsoft eventually delivered support for Safari a year later, and today the company confirmed support for all browsers, including Firefox, for their web app.
The news is confirmed in the recent Skype 8.78 changelog which notes:
Skype for web: enabled on all browsers i.e. Firefox
At present, if you go to web.skype.com using Firefox, you will still receive a warning that the functions are limited, but it appears everything is otherwise working as intended.
Microsoft recently said they aim to deliver an improved, faster and more attractive Skype service in the future. Read all about their plans here.