Do you donate money to your beloved alma mater? Before you write your next check, you may want to consider what happened to Bob Garthwait, an alumnus of and major donor to Pennsylvania’s Gettysburg College—and until this week a college trustee.

Mr. Garthwait resigned from the board Tuesday after a photo emerged of him as a Gettysburg undergraduate in 1980. He was at a theme party based on the classic sitcom “Hogan’s Heroes,” and Mr. Garthwait was dressed as a guard at a German prisoner-of-war camp, complete with swastika armband....