Min-Wax makes a wood conditioner, just for the purpose of preventing the splotchy look, associated with these types of wood. It is not a "finish sealer" it is a "wood conditioner". My bad.
I tried to emphasize that this is not for nice walnut, curly maple and those types of wood. The wood on that rifle "is" similar to a book case.
Those types of wood used on lower priced stocks, have a lot of circular grain showing, and it is visible on this stock. It will be even more visible if a med. to dark stain is used. Maybe not so much with a light stain.
I also mentioned trying it on some scrap wood.
I have used the described method on modern guns, with great success and they did not look like book cases.
Disregard my recommendation, and you'll likely see a book shelf "look".
I looked it up and it did say conditioner, (not Sealer). sorry for the mistake.