I wonder if it refuses to function because of a lack of third party cookies. This is what caused it to fail for me on Safari.
Allowing third-party cookies solved my problem (but create others, of course).
It says browser not supported, must use Edge or Chrome. (Pretty sure it didn't even say Safari, but I assume Facetime must have.)
That's why it's annoying really, that it isn't just not functional (or some specific feature doesn't work) unless you disable some built-in default safeguard say, it just completely refuses if it identities your browser is Firefox. Which I'm pretty sure is nonsense. Well, Jitsi, Slack, Discord, Zoom don't have a problem implementing chat & video conferencing in FF.
I assume they're both doing something unfriendly that Firefox disallows on privacy or security grounds.