Shurtz' status as a public employee is irrelevant. Employers, whether private or public, may implement policy or code of conduct for employees. Such policies can and often do incorporate behavior outside the workplace. The questions are whether UO has such policies in place, whether such policies are lawful and consistently enforced, and whether Shurtz violated them.

Your position on blackface is similar to oft-stated positions on the Confederate flag, and contains the same fatal flaw: it assumes intent on the part of the actor. You don't know the motivations of everyone who might wear blackface and your presumptions are therefore invalid.