First, I don't believe in God, so this isn't a matter of belief but a matter of definition. Second, I have no problem with God creating a world where the princ

First, I don't believe in God, so this isn't a matter of belief but a matter of definition. Second, I have no problem with God creating a world where the principle of contradiction doesn't hold. What I have a problem with, is God modifying a realm that depend only on a set of fixed definitions. This is not impossible, this is unthinkable. Also, we have complete control over such realms. These are just concepts. There is no notion of "can" or "can't" there. Mathematical realms are just self consistent. By definition. So, talking about what God "can" or "can't" do in these realms is meaningless.