ZImbra on CentOS4 works fine, I use it myself for my own server.
I've just done a login to that account and it works fine, slightly slow on my system as it's a VM but I'm in - send me a test message and I'll reply if you like. I have a clean(ish) copy of IE6 & XP with no firewall and no additions for IE. Do the users that have IE6 have it up to date, all service packs applied?
How much memory do you have on the server?