I'm not sure what the difference is between sites "not working" and "breaking", but as a counter point, I've seen neither in the past three or four years of exclusively using Firefox as my web browser.
Been using Firefox forever, since it was called Firebird, migrated to it from Netscape at some point.
One example of a page that doesn't work is Amazon's "Today's Deals"[1] page.
[2] is screenshots of the same page in Firefox (top) and Chrome (bottom). I do have uBlock Origin installed but disabled for Amazon.