Controversial topics are relevant by definition. They inspire emotional, dramatic responses, and isn’t that what radio shows want? But many stations and shows try to avoid sensitive topics because they fear complaints. But you don’t have to be controversial. Just use the topic as a background for the entertainment value in the foreground This aircheck from Tad, Drex, and Kara at B98.5/Atlanta is a great example. The topic is controversial (vaccinations), but the AC station had no negative feedback.
Example: The Topic Is Controversial But The Entertainment Is Not!