Whitewash originally had several specific uses. Primarily used inside barns, it reflected more sunlight in the barn, before electricity. Thereby giving more light for animals and chores. Whitewash offers some protection from bugs, discouraging them from borrowing into the wood. And it also deters some moisture. Barns simply worked better and lasted longer when you used whitewash. And it was/is simple and cheap to use. Just mix hydrated (not regular) lime with
water, for me warm water works best, and "paint" it on. For longer lasting ww, add some (unmolested) whole
milk.
So to your "problem". Are you trying to mimic the look of a whitewashed barn? Help preserve the wood a bit? Add light? Or is it just an esthetic question? ~For me, in Ohio where we have winter, I like the warmer feel of natural wood. White walls just don't feel warm to me. We have some 40 buildings here, some are paneled, some are white painted plaster board, many are painted with colonial colors. Darker shades of paint or wood tend to show less spider webs, and wear and tear, and dirt/fingerprints.
~~I'd go natural wood. Start with natural wood and you'll always have wood. Start with painted or stained wood, and you'll have a heck of a time going back to natural.