Glad to be here!
This is meant to be proof of concept, I won't take it further unless it's acceptable. It edits the source (before FF sets about processing the response data) and removes 'crossorigin' from the script tag. I think Thomas had said that removing the attribute doesn't work; but in this approach it does work on the test page code (which I used on localhost) shown here https://git.synz.io/snippets/3
The regex is faulty and needs adjustment! ...because it also deletes 'crossorigin' from unintended places. Pardon me, but I really dislike composing regex. It is meant to replace 'crossorigin' only when found within a script tag.
Won't work on jsFiddle because of how things are nested there. Not tested extensively in the wild. It needs also to handle large pages as demonstrated at: https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/WebExtensions/API/webRequest/StreamFilter/ondata (the 2nd example there).
It might be possible to edit the data without filtering (and thereby be faster), as done on an MDN example.