Opera is fully compatible with everything you could possibly wish to do on the Wmich websites. That includes wmich.edu as well as gowmu.wmich.edu.
However the biggest problems you will encounter using Opera is with gowmu - because of the way it "sniffs" for browsers. It is only rejecting Opera because it sees that it's not on its "approved" list of browsers. But once you get around that, everything works - which tells you that GoWMU is arbitrarily blocking Opera - basically sending it different (read: broken) code, so that things don't work the way they should. The same thing used to happen with MSN.com, until Opera sued their ass off.
The way to get around this is to "spoof" your browser identification. You can do this by pressing F12 and changing from "ID as Opera" or "ID as IE" to "ID as Mozilla". When you tell them that you are Mozilla, they will send you the right code, and everything will work. The longer term workaround for this is to add a line to ua.ini - which is found in your profile directory (to find this on your computer, type opera:about in the address bar and look for "Opera Directory").
At the bottom of your ua.ini file, add this line: wmich.edu=2 - that will allow Opera to ID as Mozilla just for that site - and that setting won't change when you adjust the global setting via F12.
If you don't want to keep getting that annoying page saying "your browser is not supported", just bookmark this url - http://gowmu.wmich.edu/cp/home/check/pre?optInSupport (right click and "bookmark link"). If you go to GoWMU via that link, you'll never see that annoying page again.
The broader issue though, is that Western should support Opera - it is a fast, secure, easy to use browser, that will be gaining a great deal more market share in the coming months. In practical terms, if Western's tech support department doesn't want to start getting unnecessary calls about this, all they need to do is stop "sniffing" for Opera. Their developers can start by having a look here. While that is taking place, I'd be more than happy to help them develop a page on their tech support site that deals with Opera - including using M2 (Opera's mail client) to read wmich.edu e-mail. The content of this post is free to be redistributed, in part or in whole - as long as you link back to me and give me credit.
Can anyone say Fanboy?
Edit: it appears I should have done a bit more homework - wmich.edu=3 (IDing as IE) actually works better - you don't have to use the workaround url.
For all the people still using FireBadger, the url to avoid the unsupported browser page will work for you as well. But if you move to Opera, you don't have to :).