That will teach me to read properly.

I've no real idea, but I suspect that they would all come from the supplier in the buff and the recruit's first task would be to apply the relevant colour as part of the 'bull, blanco and brasso' system.
Going back to the OP though, it would depend upon how rigidly the rules were applied. If your RSM or Colonel was a martinet, he'd insist that the regulations were for white (or black etc) equipment and woe betide any man who did different. A more practical commander might be a bit less stiff on campaign, but even as late as the 2nd Boer War, the outline of a soldier's equipment provided a convenient aiming point.

These men were photographed in Cardigan on their return from South Africa in 1902. Their equipment is white, but use has worn it back to the buff in places of heavy wear. This implies that regular blancoing had stopped, but there appears to be no effort made to 'camouflage' the equipment.

Whether they are wearing worn-white, or 'tea-dyed' equipment, this Maxim crew's equipment is clearly much lighter than their uniform, which itself was much lighter than the later 'khaki' in general use (as in the photo above).
Bearing in mind that all the photographic evidence shows lighter equipment, or darker if it's brown or black, and the original picture is an 'artists impression', then the reason why most people paint their equipment white or off-white is because it was.
