This is just a guess but I think the stock may have had an oil of some kind applied to it at one time.
If this happened, the oil base stain you are applying will not sink in. If it doesn't sink in, it wont stain the wood.
This oil on the wood may be just from a lot of people handleing the stock and the oil is from their hands.
As you applied an oil base stain (minwax) the stock wood definatly won't "take" a stain of any kind now.
By the way, some woods are naturally oily and as we don't know what kind of wood it is, that may be your problem.
Several things come to mind to fix the problem.
The most obvious and best method is to resand the entire stock to get down to raw unoiled wood. If this is not possible because the wood is finished flush with the furniture (butt plate, nose cap trigger guard etc.) and can't stand to have that much wood removed, or the wood is naturally oily, then the chemical approach is the only way I can think of.
When I say chemical, I am not refering to paint remover. That stuff only softens the paint it comes in contact with and will not soak down into the wood where the offending oil is. Don't use it.
My suggestion is First: Buy some WATER BASE STAIN like Birchwood Casey Walnut. It is usually available at Gun Stores. If you can't find it, we can tell you where to call. Just don't use any more OIL base stains.
Next, try some DISK BRAKE CLEANER. Spray on a lot of it so it sinks deeply into the wood. It may take several coats. Dont do this inside your house. Let it dry outside between applications.
After several coats of break cleaner, try the water base stain on a little spot and see if it "takes". If it does, your in business! If it doesn't then you may have to try Acetone, Lacquer thinner or Carbon Tetrachloride (if you can find it). After you apply several coats of one of these, try the water base Walnut stain on a little spot again.
If it still doesn't work you can try the Lye treatment.
I saved this for last because it is dangerous to your skin, hair, eyes and any other thing made out of body parts including your dog. This is serious stuff. It will desolve anything you are made of. Keep some vinegar handy to splash on you if you get splattered. You WILL know where to splash it because the spot will feel like it is on fire.
Lye can be found at hardware stores. It is used as a drain cleaner because it eats just about anything that is not wood or metal.
If you try this, buy some of the surgical gloves at the drug store (to protect your hands). Wear an old long sleeve shirt and WEAR GLASSES!!! If you don't own some, buy a cheap pair. Even sun glasses will work. Just wear glasses. If some lye gets in your eye, it can distroy your eye before you can neutralize it!!!
Mix about a tablespoon of the dry lye into a cup of water.
Use a NYLON paint brush and brush on at least 5 coats letting it dry between coats.
Try the water base stain on a little spot again. It should "take". If it does, you will need to neutralize the lye.
As lye is a base, you need an acid, and the best one for this is several coats of vinegar applied sopping wet.
After the last coat of vinegar has dried, lightly sand the wood (to remove the little raised fibers it will have) and proceed to apply the Walnut stain to the full stock.
If this doesn't work, either paint it with camo paint or say to yourself, I always kinda liked blond wood.