“Family Guy,” the Fox animated comedy series, is either irreverent or crass, depending on your tolerance for unmannerly humor. Viewers come for its pop-cultural free associations and flatulence gags, not necessarily to debate pressing issues of the day.

So it is probably the last program that anyone expected to serve as a catalyst for a continuing fight about the depiction of disabled people on television, and whether they are fair game to participate in and be the subjects of satire.

It is a dispute that has drawn in Sarah Palin, the former Republican governor of Alaska and 2008 vice-presidential candidate, who has a son with Down syndrome, and a “Family Guy” voice actress who, like the character she portrayed on the show, also has that disability. Though the two women would seem to be coming from similar perspectives, they have ended up as far apart as possible.

The argument was started by a “Family Guy” episode shown on Sunday night, in which the teenage character Chris woos a classmate named Ellen, who has Down syndrome. During a dinner date, Chris asks Ellen about her family, and she replies, “My dad’s an accountant, and my mom is the former governor of Alaska.”