Have you complained? It's the only way to get things to change. It's obvious that if simply setting the user agent makes everything work, that there is no valid reason for them to attempt to make you use an insecure and buggy kludge like IE on a banking site.
Yes, by phone & email. They said the site would work with Netscape. My complaints that Netscape and Firefox were essentially the same browser meant absolutely nothing to them. Then they told me they would be glad to help me "upgrade my browser" so I could use their site (at which point I hung up). If it wasn't so much trouble, I probably would have changed banks over that.
That was the event that prompted me to go looking for the agent switcher. I knew that if the site worked with Netscape, there was no reason it wouldn't work with Firefox. I have otherwise been happy with Suntrust Bank, but their online support people are either totally computer illiterate or a bunch of aholes (most likely both).