Firefox has a built-in list of websites that need UA tweaks to work in Firefox. (In fact, Firefox's UA override feature was designed by ex-Opera engineers at Mozilla.) You can review the list (and toggle them) in Firefox's about:compat page.

A recent success story: Mozilla recently added a UA tweak to work around Slack's Chrome-only check for video calls. Slack engineers reached out to Mozilla and, just a few days later, Slack removed their Chrome check and now support video calls in Firefox without a UA tweak. :)