Is there a reason for the bleached white flour? Will unbleached flour change something?

By the way, if this is your taste in pie crusts I'd recommend looking into Rose Levy Barenbaum's "perfectly flaky and tender" ppie crust. Kind of a weird recipe- it's mixed in a plastic bag (I think there's also a food processor version) but it handles beautifully and indeed does make an extraordinarily flaky and tender crust- too much so, for my taste- I like a crust to have more bite- but it certainly succeeds at what it sets out to do.

I do recommend bleached flour for the most tender pie crust. Here's more info on the bleached flour—one of the 5 tips for success that I gathered from Stella (and my experience) and linked on the recipe page: https://food52.com/blog/23402-genius-no-stress-flaky-pie-dough-recipe-tips

You should be fine with AP flour. The bleaching process lowers the ph in the flour which does soften the protein a bit. Its extra insurance against gluten formation, but its not at all necessary. In fact, I use bread flour in my pie crust, and its never ever tough.

Bleached all purpose flour because there is less gluten formation (leading to tough crusts) since the protein content is lower than the unbleached. Results are a tender crust without the stress of overworking the dough. I think you can still use unbleached AP flour, but you'll have to be mindful of how much you work the dough, which sort of negates the "No-Stress" part of the recipe.

Just having read Stella Parks' cookbook, I'd be willing to be that she's calling for bleached for a reason. I even recall reading a reason but unfortunately I don't have the book here. I'll try to remember to find it when I get home.

I'm a little vague on the chemistry, but bleached flours are generally regarded as softer than unbleached and are preferred by some for pastry making.