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.