That's a good question... And I really am not sure.. What I do know is:
Corporate logos (or even having the name of the corporation written out) is a no-no. Hence why Tastefully Simple came with "T.S. (heart)s Bob" shirts (even though they didn't catch Anita saying Tastefully Simple while on stage).
College shirts, of course, are not only okay, but I am convinced there are hidden vendors standing around selling them before every taping...
Sports jerseys are okay. Over the years, I've seen contestants in pro jerseys, including a Ten Chances winner in a Mark Grace jersey, and a recent contestant in a Brian Westbrook jersey.
T-Shirts depicting musicians - even incredibly famous ones - seems to be no problem. Starcade and I both saw a contestant (a showcase winner, no less) in a Tina Turner shirt on a show that aired in November.. And they haven't batted an eye at me any of the three times I've shown up - complete with that other Madonna on my shirt (though I would imagine if I were spinning the wheel, and gave a "shoutout" to Sherrie Austin and Madonna, they would not be too amused).
Saying who you work for on the air is a no-no, even though "Tastefully Simple" slipped by them...
And, of course, you can't be a contestant if you're RUNNING for public office (the "George Takei rule" as I call it)...
But I've never heard anyone mention a non-profit organization.. They really don't specificially mention them while going over the rules.. I've never even encountered anyone who is curious. Best thing I can suggest is contacting CBS and asking, unless someone here might know for sure.