The fact of the matter is that there are basically two relevant families of browser engines in the world today: Webkit based, including Google’s Webkit fork Blink (Safari, Edge, Chromium and derivatives), and Gecko (Firefox). I’ve got a lot of respect for Firefox, but the majority of web users and the majority of attention from web developers are on Webkit and Blink, especially Chromium based browsers, these days.
As @Mik mentioned, there are Chromium based alternatives to Chrome, including ungoogled-chromium, that will run the Polkadot extension just as well and also provide good compatibility with the Playground, without the Google spyware.
If there are issues running the Polkadot extension on Firefox, maybe someone experiencing the issue can open an ticket for the Polkadot team on their extension repo?