The Navy had a penchant for whitening all of their webbing for some reason. Even on the RN/RAN/RNZN officered inshore/coastal patrol boats that used to patrol the straits of Malacca and right up into the S-China sea had white webbing. Not whitened as in whitened of course but just left to bleach in the sea water and sun. So I'd say it'd be like that in real life on the ships. Mind you, if your man was the Orderly Officer, who'd just fallen out of the Officers Mess at 5 to 10 to inspect the night guard before retiring - back to the Officers Mess bar - it'd be gleaming white!