I regularly raise the issue of when is money to tainted for a nonprofit to take (like this week's case of nonprofits that received monies paid to celebreties by members of the Gaddafi family).
It appears that Michigan State University has one standard it uses for certain: when the gift in question, or the organization, taints the institution, don't maintain a relationship and I presume, don't accept their money. The nonprofit the University is avoiding is one of its very own booster clubs, the Downtown Coaches Club. The Club is under state investigation for lottery (aka gambling) activities according to the Washington Post.
I would hold out though that the question here is not whether any gift money is tainted, it's whether the Univeristy needs to maintain an arms-length distance from what might be a tainted organization. Hm...now that kind-of changes the conversation about tainted money. Perhaps there is no such thing as tainted money, just tainted organizations which, when there is a relationship, taints the beneficiary.