It is one of those "unofficial" rules based on unit or branch/corps tradition. I have never seen an RSM wear low shoes on parade just officers. For officers, I would check with the Adj and they will sort you out.
Almost every parade instruction/Admin O I've seen over XX years has said "officers shall wear oxfords, NCMs shall wear ankle boots". Recently I was part of a mil funeral @ the NMC. As there was no instructions otherwise, I wore short sleeve shirt and oxfords and some people thought that was odd. Just tells me most people just aren't aware of para 5(b)(2) at link below.
shall be worn by Navy members, and
may be ordered worn by Army and Air Force members.
OldSolduer mentioned "the CO can order" aspect...265, Ch 1, para 8:
8. Control is exercised by local commanders who may standardize the dress of subordinates on any occasion, including the wear of accoutrements and alternative or optional items, subject to overall command direction.
** just to mention, there are other dress instr's to read/consider. I'm a 1 Cdn Air Div type, so operational dress is governed by a CADO, and then I have my Wing Dress Instr's to know/consider as well.
The actual dress regulations say that either oxfords or ankle boots can be worn, but that ankle boots are the normal footwear for parades. This does imply that oxfords are normal footwear for other, unstated, duties. The dress regulations do not indicate an officer/NCM divide on the subject of footwear. And since officers and NCMs are issued with both, the implication is that they can wear both, depending on the circumstances.
If the various Corps and Regimental Senates find this situation distasteful and offensive to tradition — they are free to staff amendments. The dress instructions devote 7 pages to the subject of aiguillettes — there is room for another sentence on shoes.