Q: Is FamilySearch currently having issues with Firefox? A: Yes.
If you are here because you are having issues with FamilySearch in Firefox, I'd like to say that you aren't alone. A number of folks have posted problems about FS pages being broken in Firefox, most often when trying to attach records but also with merge and other actions. If you do a Forum Search for Firefox and then Sort By Date, you will find kindred spirits who are experiencing what you are.
In my case, the issues were consistent on Windows 10 and 11, on the following 64 bit versions of Firefox: 91-94. I also had identical issues with a clean install of Firefox 78 ESR, with no extensions. However, another user found that 78 ESR worked well for him. I think it's worth trying.
Here's the important part.
In chat, I was told that "Some FamilySearch features do not work in Firefox currently. Chrome and Edge are the browsers with all features." which was very helpful. This at least tells us that the Firefox issues are acknowledged. I'm confident the dev team will get it worked out.
That is all.
notes: I occasionally found temporary relief using a Private Firefox Window in all of the above versions.
I am presently using Firefox 68 ESR and am not having any FamilySearch issues. However, 68 automatically updates to 78 on launch. I can prevent the update but the method is fairly onerous (req policies.json file). ESR 68 is pretty old tho and some sites struggle with it (eg: Ancestry).