In recent weeks, Tucker Carlson, the conservative Fox News host, has challenged the Black Lives Matter movement, dismissed demonstrators as “criminal mobs,” accused a Texas police chief of “sounding more like a therapist than a cop” and mocked a CNN children’s special about racism that featured Elmo, the “Sesame Street” puppet. His comments have generated a harsh backlash. Critics have called Mr. Carlson’s on-air monologues incendiary and accused him of making racist remarks. Major advertisers, including the Walt Disney Company and Sandals, the vacation resorts, have fled, requesting that Fox News remove their ads from Mr. Carlson’s 8 p.m. hour....