You can bring a parachute in your carry-on or checked luggage. Just make sure the rig is separated from other parts of your luggage, and arrive half an hour early in case the TSA wants to ask you some questions. Yep, you can bring your pie or cake through security, though it might require a little additional screening.he TSA says fishing rods are allowed on as either carry-on or checked luggage, but ultimately the decision rests with your airline carrier. So before you trek that fishing gear all the way to the airport, just make sure you can actually bring it on the plane.