When you start to add conditions/exceptions to free speech, it ceases to be free speech. Unpopular speech, however painful/nauseating, is explicitly protected in the U.S. If all speech was agreeable, there'd be no need for free speech laws.
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."