Which is probably the CO, in fact its probably not even the current CO, its probably one from yonks ago and CO's haven't bothered changing it
There is no hard fast reason to wear or not wear them, the Royal Regiment is unlike many Corps who put out a Corps directive to wear them, instead its left to the CO to decide on some matters of dress, this leads to a certain level of individualism. When I joined up in '87 there were so many different combinations of dress it was confusing, some wore green plastic, some wore RA stable belts some wore personalised Battery or even regimental level stable belts. There were backings to cap badges, cloth capbadges, some wore titles, some didn't, some wore "pillow" stripes, some wore No2 stripes, there were blue jumpers and thunderbird hast and don't get me started on the jock regiments and their epaulette slides.
In the early 90's it changed to a much more regimented (or corps like) uniform, I almost cried when I removed my cloth cap badge and replaced it with a plastic one (
But in the last 10 yrs or so the trend seems to have returned. ah vive la difference
Now why is it that a TA unit doesn't wear stable belts ? Simple, its all about cost, you have to buy the things and its hard enough to get young uns in the regs to buy the bloody things, let alone in the TA