Firefox does not accept ⌃⌘Space keyboard shortcut for Emoji & Symbols
Solution 1:
It is a known issue: https://bugzilla.mozilla.org/show_bug.cgi?id=1563862
However the issue is closed, and based on the comments it looks like it is related to the language of the browser.
As far as I can see the Firefox can be downloaded in different languages, but also language of the UI can be changed after. Also, it looks like if you are changing the language compared to the default the Emoji shortcut stops working.
So your best bet is to download Firefox in the language you are using it, instead of changing the language afterwards. Or you can always try to go to Preferences and change the language to the one Firefox was downloaded in originally. It may also matter to have the language of the System and Firefox set to the same.
In my case if I set Firefox to Italian the shortcut stops working, but if I set it to UK English, it starts to work (after restart). I assume it is because I've originally downloaded Firefox in English.
If you don't want to do that another workaround I've found is to go to System Preferences… > Keyboard
and on the Keyboard tab turn on the "Show keyboard and emoji viewers in menu bar". With this there will be a flag icon in the upper right of the screen, where the Emoji viewer can be opened, just like as if it were opened using the ⌃+⌘+space shortcut. Bit more cumbersome...