What should you do when you anticipate that a topic of discussion is likely to cause concern or discomfort to at least some of your students? What should you do about your own feelings, especially if you feel strongly about the issue? Should you keep them hidden?
There are benefits to be gained from setting ground rules for any class, irrespective of whether you expect controversy or not. (From the pull down menu, I recommend Brookfield and Preskill's method of setting ground rules.) Setting ground rules in advance can help to restore civility and decorum in case something should happen to disturb them.
The article Teaching Controversial Issues talks about how to prepare the ground work ahead of time if you know controversial issues are going to be introduced. This involves understanding the developmental stage of student thinking, what kinds of issues might cause controversy, how to lay the groundwork for such discussions prior to their occurrence, and how to moderate them.
Sometimes some major issues come up in the news (such as a war starting or 9/11 or the tsunami) that are of deep concern to many but are not part of the course. Should you ignore them? Should you briefly acknowledge the existence of these issues and then move on? Should you have a full-fledged discussion? This article has suggestions for how to plan for such classes and also how to deal with it if a student suddenly raises it.
There are times when an explosive or disturbing issue comes up suddenly in a classroom and students might get very angry with each other or with the instructor. Then the instructor has to go into conflict de-escalation mode. This article deals with an actual case of sudden explosion caused by a remark about race and how the instructor managed to calm things down. It also addresses the important question of how instructors can best deal with their own strong feelings.