Antlers naturally bleach out to gray/white as the age and are exposed to the sun/weather. That tan/brown only stays with them if you keep them out of the elements (mostly sun). And the natural "oils" in the antler also dry out. Neatsfoot oil helps restore some of that. (also other animal fats/oils)
Scrub and wash them. That will get any surface gunk off. If you then want some of that "natural" tan/brown color, brush them down with a solution of potassium permangnate. It will turn organic matter to different shades of tan/brown. It looks like purple when you put it on, but dries tan/brown. But it will also stain your hands or wood tables/counters if you get some on them.
Yes, interesting things show up at those flea markets, garage sales, and "tailgate" sales.
Mikey - that grumpy ol' German blacksmith out in the Hinterlands