Another option is to add a very small amount of white pigment to your finish for use as a toner (e.g., 1 oz per gallon). This masks the wood grain slightly, but makes the white stain look much brighter/whiter. The same technique works for other light colors as well.
What did you expect when you stained a wood white that had browns and red in them? Do you realize that the color of the wood still comes through even though you are putting another colorant on it? Unless you are using a highly pigmented opaque primer you are only changing the wood color and not hiding them. Hopefully you will learn from this and start your projects with a substrate that is suitable for the finish. Next time do sample boards so you can see what your results will be.
I did offer some help. Do sample boards. Use various substrates. Adding green to get red out only helps some of the wood but what happens to the wood that doesn't need green? It turns green. Now how do we get the green out?
If you are going to get into finishing and particular staining, you need to practice and see for yourself what these products do. Like when the clears wet out the wood and totally change your color after you thought you had it matched perfectly before you clear coated it. Practice, unlike what Allen Iverson said, is what is needed.
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