Had the same rattle on my passenger door. Found a thread on another forum that said to adjust the U striker 1/8" inward toward the seat. I loosened the two striker bolts, made the adjustment and whalla! The rattle is gone!
2013 Rubicon Black 2dr "Lil Mule", 2.5" Rubicon coil lift, 33" Toyo Open Country A/T II, Ultra Bolt 198 17" Rims, Cobra 75 WX ST CB, Portable Cobra 38 WX ST CB, Mopar HD Rock Rails, MOPAR Mud Flaps, Mopar Front Skid Plate, Windshield/grill Mounted KC SlimLites 6", Bestop Floor Liners, 14" AntennaX Antenna, Scott Drake Black Billet Shifter and 4x4 Knobs, Mopar Exhaust Tip with trail scratch, aFe Dry Filter, Dirtydog Sun Shade, Diablo Sport Trinity (87 octane performance tune).