question about carrying reels on flights to Mexico...

am going to comedero next month and flying American airlines...Atlanta to dallas and dallas to mazatlan...and returning same way...
don't want to put my reels in checked bag because of theft possibility but have heard that if you carry fishing reels in your carry-on bag,you have to remove the line...
anybody had any experience with this?....

Yep...my last trip to Mexico I checked my large bag with baits/hooks/gear and a tube of rods (which is no longer necessary for most lodges because they provide them) I loaded all of my reels in a cushioned camera bag with dividers and hauled it around as my personal item with a roll aboard containing my clothes. Not a problem.

On my way back from Oviachic the Mexican Federales went through my truck and boat. I was "detained" when they found bullet weights in my tackle box. Took a while showing them how they were used before they decided they weren't dangerous.