No, you cannot request a white bun (well, you can but the answer is no).
Which has been my complaint all along. Bring on those lousy wheat buns that some hate and some don't have a problem with. That's fine. But give us a choice! Kids get a choice on their meals. Fries or carrots (or something else healthy). Soda or milk or water. We get something that a lot of us find not appealing.
And Disney World is losing my sales of hot dogs and that's a lot of them. I don't even want a cheeseburger there anymore. And forget the pizza if the crusts are changed. And if they EVER change the soft pretzels, I'm turning in my annual pass.
Too bad the McDonald's at the parks don't serve burgers because I sure the heck would be over there. And I swore I would never buy anything from a McDonald's in any Disney park.