Not a great example, but the ERP I use for work doesn't support Firefox and has some minor issues due to how Firefox handles frames differently from chromium based browsers.

If you use a browser back, the site goes all the way back to the home page instead of the previous menu you were using, because they put a whole extra layer over the entire site to handle navigation.

I haven't noticed a website outright blocking Firefox in a while, in part because Firefox devs are staying on top of it with overriding a lot of site blocks. The issue I run into the most is reduced video quality in Google Meet in Firefox, so I switch to Safari or Chromium when I need to do calls there.