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I don’t know where you are located, but I have been stopped 3 times, since I have had my LTC. In each case I simply handed them my LTC with my DL, they all gave it a cursory glance, handed it back, and two asked about the location.
Not one attempted to disarm me, or had any issue with the fact that I had a gun.
As a former LEO, I can tell you digging around in a console, or glove box, makes them nervous. Keep your hands fully visible, until asked for any documentation. Then tell the officer where it is located, whether in your pocket, glove box, etc.

I’m not sure why these particular LEO would go to the extreme to disarm you. Handling a loaded gun, creates more risk, than leaving it alone. A Texas LTC, lets the LEO know, that you have passed a background check, and a proficiency class. I have not heard of many cases, where an LTC holder, was disarmed during a traffic stop. The LEOs you spoke with, definitely don’t fit the norm, and I have spoken with several, regarding, LTC, OC, etc.. and even while OC, not one have made any comments similar to the ones you describe.