There are some styles of HOLSTER that make the Glock discharge. I the Serpa, as sort of noted, can be one. The other escapes my memory right now, but it's a leather holster that is worn OUTSIDE the waistband but INSIDE the belt. It has a piece which can impact the trigger after the pistol is broken in.
Those carrying them WITHOUT holsters just need to be educated. These things have no real safety and are literally half-cocked.
Full story here: Man’s Leather Holster Causes Accidental Discharge
It would be almost like carrying a 1911 with the safety off and a round chambered. You still have the grip safety which blocks trigger movement, but the only time I've read about this being done is during CIA assassination ops where the primary weapons were knives and the pistol was to be used only if discovered. Extraction was usually covered by a sniper at the chopper and he was the sole cover to the retreating CIA team. How much of this is true, I do not know.
A 1911 is fairly safe Mexican-style carry. I've done it, but it's not my favorite thing to do. I prefer a 1.5" width tool belt and a Null Super Speed Scabbard:
Not much to go wrong there. Horsehide stands up to a lot more than bovine leather, too.
I trained on a Glock 22. I did not care for it much, though the NY trigger improved its crispness somewhat.
Regards,