GREENCASTLE, Ind. — When a psychology professor at DePauw University here surveyed students, they described one sorority as a group of “daddy’s little princesses” and another as “offbeat hippies.” The sisters of Delta Zeta were seen as “socially awkward.” Elizabeth Haneline, who was among those evicted, said, “The Greek system hasn’t changed at all, but instead of racism, it’s image now.” Worried that a negative stereotype of the sorority was contributing to a decline in membership that had left its Greek-columned house here half empty, Delta Zeta’s national officers interviewed 35 DePauw members in November, quizzing them about their dedication...