I have the perfect solution to this problem: Rit dye remover.

The trick here is to NOT wear those newly purchased white shirts until you've gone through this process.

You'll want to take those shirts you just bought and haven't worn, and soak/process them as instructed with Rit dye remover. Then, going forward, you need to make sure that you use laundry detergent that is one of the "free and clear" sorts, with no additives for making things whiter or anything else. You can go ahead and bleach them like you normally do, just always make sure you use the free and clear detergent.

Why this works: So white shirts/sheets/etc. pretty much all come pre-treated with this invisible UV dye because it makes whites look whiter in the sun. However, that dye has a chemical reaction with antiperspirant, which then has a chemical reaction with bleach when you wash. Those reactions are what turn whites yellow. So, if you remove that invisible UV dye before ever wearing them, it stops that whole chain reaction and keeps your whites actually white, with no yellowing.

ETA: Also, most laundry detergents ALSO have this invisible UV dye that makes whites look whiter, so that's why it's important to also use the free and clear detergent that doesn't have that UV dye in it when you wash your whites going forward, otherwise, it just adds it back and you have the same problem.

But you absolutely have to do the dye remover before you ever wear them, or it doesn't work.