As far as I know (which ain't much) the red tag is part of a larger plastic moulding that fits in the chamber. It has the dual purpose of ensuring a round can't be chambered and giving a visual indication that the weapon is safe.
You haven't missed the point at all. They know sweet FA about berets and IDF regulations require them to be under the epaulette most of the time (the fold this requires is clearly visible in many of their berets). You may also have noticed that the uniforms aren't particularly smart and medal ribbons barely exist.
On the parade ground they can barely march at all. When my son passed out of infantry NCO's course last year the entire parade consisted of just 20 paces forward, marching on the spot and halting. Having grown up on a diet of trooping the colour I personally found it excruciating but hell - if they're sufficiently professional soldiers and can defend the country - who needs that stuff anyway?
The current CGS in working No. 1 dress order - open neck shirt. 40 years of service and almost no medals.