Good question. I have traveled with rods in plano tubes and I have taken them along as carry on but where checked at the gate. I'm not sure that airlines do that anymore. I have checked in fishing lures and have had no problems. One thing you have to consider is properly packing your gear b/c if not rods can bend or break, and fishing lures can be damaged during flight.
I have always wondered what they would do with fishing lures in a carry-on bag?
It was a different world when we were boys and girls....