I harrass support in cases like this. Like, are your web developer people completely incompetent?! It's not like making things work in FF takes some real big effort, just do everything properly. (We develop a lot of web products, so this isn't some baseless statement)
That stinks. But I’m surprised. I went back to FF full-time in 2021 and have seen almost no compatibility issues with websites.
Did you report those sites to https://webcompat.com ?
Also, did you try disabling Enhanced Tracking Protection for those sites? (Shield icon in URLBar)
Try in a fresh profile (via about:profiles)? (Sometimes people tweak a lot of about:config settings, which is generally NOT a good idea - there are no guarantees for those.)
Run multiple browsers. I have Chromium around just for banking and problematic e-commerce sites that can't tolerate my security posture.
well as an individual data point, I recently threw in the hat because both my regional bank's website and my health insurance page stopped working at all on Firefox. Not really something I can do without and it seems to be getting worse for companies with smaller web presences.