For some reason, Key Bank won't let me login using Firefox unless I spoof my user agent. They claim it's due to security issues with the browser. This is more of an active check though. when I pretend to be Chrome using as different user agent in a container, everything works fine.
Also, ADP (timesheets and paycheck system) frequently breaks for Firefox. Sometimes it just won't load any of its forms or grids when I'm using Firefox. I think they only test with Chrome.