I have one place that says Firefox is not one of their supported browsers. It doesn't actually stop it being used though. They go on to say that the session will still be secure but some features of the site may not work. It all seems OK to me. I have emailed them saying it's about time they did support Firefox since it is becoming a popular browser and thought to be very secure. They have acknowledged the message but haven't removed the notice yet.
Strange how they support IE even though it has had security bugs but won't give other browsers the same support. I've been using Firefox at this bank for a few years now with no problems. Other financial establishments I deal with don't question Firefox at all.