As other comments have pointed out, Firefox doesn't necessarily support the necessary APIs that Discord is using for this. I have the same issue where neither Firefox don't support the in-browser MIDI API, so I need to have Chrom(ium) for a webapp that lets me configure some MIDI hardware that the manufacturer provides zero computer interface for.
I'd like to use Firefox for everything, but there will always be some edge cases like this as long as there are APIs or other features that it doesn't yet support. Of course not to say that securely implementing every new API is trivial, but that's just how it is right now