As you can see from the code in my post, the script runs, but the server responds with a 403 error. That looks more like the JS is doing the wrong request in FF. The problem seems to be the referrer. For comparison:

Referrer in FF:

  https://sheets.googleapis.com/v4/spreadsheets/1A3xz8NFWjebuMbGWvy2yUBKcnAmuZSs5JmKq9-JDss8/values/Email?key=AIzaSyCxiboNdLE5nSch2pdwI3blsfvfyss3Y0M

Referrer in Chromium:

  https://secured.fyi/

Btw. I tried deactivating any Addons which might interfere with the requests but it didn't change anything. So probably all users with a modern Firefox will have an empty table.