I too experience privacy extensions breaking websites frequently, since I'm a heavy user of those, but so far I have never encountered a case of a website that was truly broken under Firefox. It was always one of my settings and worked under a clean profile.
They didnt release the specifications early enough for people to rewrite their addons and at the end of ESR52 there where still multiple bugs open which prevented people from porting their addons. We didnt even get a normal 1 year ESR support frame for gods sake. All that ignoring the fact that there was no warning for the end users that all their security addons were disabled after the automatic update.
I am still furious about the absolute arrogance and carelessness Mozilla showed here.
But Chrome as an alternative? That's not even on the table. Firefox is definitely the lesser of two evils.
They simply changed the default bookmark location with no option to change it back.
I need an addon to change the default bookmark location to keep my earlier filing approach.
I mean really?
I'm still upset that they broke custom keyboard shortcuts for ... two years now? All the replacements will only remap keys after a tab's JS has loaded. I used to be able to just zoom through the tabs with shift-j and shift-k, but now it will randomly stop on pages that need to reload, which breaks the whole experience.
I've had Super NES games that offered key customizations, and had much less memory and money to work with. That's really disappointing.
To this day, my browsing experience is still worse with Firefox than it was before 57, because so many useful little add-ons have never been replaced or have been replaced only with inferior versions. In some of those cases, that useful functionality can't be provided in the new environment, because the APIs to support it aren't there. I was unpleasantly reminded of this just a few days ago, when the same problem infected the latest Thunderbird update.
More seriously, I am running into increasing numbers of sites that simply don't work properly with Firefox. Sometimes this is because of the privacy/blocker extensions I use, but often the problem persists even if I disable those. Whether it's due to bad web developers doing Chrome-only things or bugs in recent versions of Firefox, the unfortunate result is still the same from the user's point of view.