I came up against this when confronted with a scratched up hardwood Model Savage 24 stock. If most of you will notice, on hardwood (non walnut) stocks from most manufacturers, if it gets scratched, the stock will be pretty white underneith. That's because the manufacturers use a combo stain and finish to give non descript stocks some charactor. But when you refinish , you'll remove all that color and you've got the problem of a piece of wood that just will not take stain very well at all. Birch and Maple, and some gum are offenders who just don't soak stain in.
I found a product at Michaels (arts and Crafts store) which is toning spray. It comes in a couple of different shades, walnut, dark walnut, and cherry. It was intended originally to spray on flowers or anything really where you wanted some wood toning. It is Lacquer, witht the stain there too. And, you can do a pretty credible job of covering a very white piece of Pallet wood with a uniform wood color, just like it came out of the factory. I found the stock looks best when completely covered without trying to show any grain. I tried to use it in a minimalist fashion, but didnt like the results. Most Factory stain jobs do not show a lot of grain, and neither will yours. But after the lacquer is very dry, lightly buff the surface with 5-0 (00000) steel wool, and spray it down with a good satin fast drying polyurethane like MINWAX. I usually do that at least three times for addeed protection. The stocks will look good, and I have had many pleased individuals when they see an old 22 or shotgun renovated this way.
(the bottom one in the group of three was recently purchased and needs some issue addressed.)