I'm old enough to remember the days when every change I made I had to roll through multiple versions of IE all the way back to 6, and different things would be broken in different versions.
(I cringe when I look at some of the emails I had with them back when I was 11, though...)
The only apps that are noticeably worse in Firefox for me are Google Docs and Google Meet.
I honestly do not know a single site that is broken with Firefox. What breaks sites is my strict DNS filtering setup, not the browser I use.
I'm running Firefox, with containers enabled, with ublock origins (and as such "somewhat privacy conscious over and above the defaults"), and this works fine for me.
There could be any number of things that cause an individual issue, which may or may not be related to Firefox itself :-/
BTW, Resist Fingerprinting's main impact (for me) has been to increase triggering of "Click and Hold to prove you are not a bot" on sites relying on fingerprinting as an anti-bot measure (Drupal, Walmart, Kickstarter). On some of those, the developer doesn't even realise that measure can trigger, and it triggers in a background XHR (Kickstarter does this sometimes).
This is still better than some other sites like Lowes and Fedex where the entire site (Lowes) or backend API (Fedex package tracking) simply errors due to an Akamai block without any option to prove yourself. For those, you pretty much just have to use another Firefox profile with fingerprinting allowed (or another website).
Intentional or not, they really contribute (in my mind at least) to the overall perception that Firefox is truly dead. Nobody even tests for it anymore, or worse, accepts that it's fine to be broken on FF.