Firefox unfriendly sites

Firefox is my browser of preference, so I get a little bit annoyed when I can’t use it with certain sites ie. sites that I would like to use.
Last weekend I was trying to use Tesco.ie and discovered that it wouldn’t work properly.
AIB’s personal banking works fine, but other areas of their site does not work, such as the business banking and the online car loan section.
Quite annoying really!