The Transportation Security Administration (TSA) has an extensive list of prohibited items but does, of course, allow travelers to bring their pets (not just service animals) through security, letting airlines decide their own pet travel policy. Reporter Patricia Marx recently tested TSA's response (as well as JetBlue's) by bringing a one-year-old pig named Daphne with her on a flight from Newark to Boston. (In this experiment with "emotional-support" therapy animals, she also brought a turtle to the Frick Collection, a wild turkey on the Hampton Jitney as well as to Katz’s Delicatessen, and an alpaca to a pharmacy—though Ms. Marx had hoped to travel with the alpaca on Amtrak.)
Ms. Marx's conclusion: "I’m pleased to report that passing through security with a pig in your arms is easier than doing so without one: you get to keep your shoes on and skip the full-body scanner." JetBlue also welcomed the additional traveler, and on the return trip from Boston, Daphne got to pre-board, where she was welcomed by the delighted flight attendants.
In lieu of traveling with pigs, those who want to save time at security or US customs (traveling internationally with animals has its own difficulties) should look into TSA preCheck and Global Entry.