Riding shoes have one important feature that distinguishes them from street or stable shoes - their heel. The heel is an absolute must for any type of riding shoe, as it prevents the foot from slipping through the stirrup.
This heel is also important if you want to combine your riding shoes with half chaps. The foot strap of the chaps is held in place by the heel.
This means that you can always wear any riding shoes with half chaps, as long as they have a heel.