University social science instructors sometimes encounter student silence or quarrels around culturally contentious subjects. In a culture that promotes distrust around the issues they teach, how do professors perceive and cope with such difficulties? Preliminary research using qualitative interviews with teachers from two different US universities explores problems they encounter and strategies they employ in the face of student struggles with nuance and a phenomenon referred to here as "polarisation anxiety." Professors strategise how to teach the complexity of phenomenon some students have been culturally predisposed to oversimplify, polarise or remain silent about.