Are Theists Illogical for Believing in God?

[Ramsin.Kh]

There is no rule that they should, you are just asserting that.

Some cross checking: If A=A is true for an electron in this universe in the double slit experiment, than what is it? Particle or wave?

All matter, not just an electron, displays wave and particle properties.
An electron is an electron, it does manifest or becomes apparent as a wave and a particle, but that does not change what an electron is.

Therefore, in this respect, all universes are logical and illogical.

Does that sound logical?

It depends, the answer is no if you consider the classical logical framework.

Say A is a logical framework build on axiomas A1, A2 and A3
And B is a logical framework build on axiomas A1 and A3
And C is a logical framework build on axiomas A4 and A5

A non-traditional logical conclusion can be made since you've used axioms in your post,
A = {A1, A2, A3}
B = {A1, A3} => A ∩ B = {A1, A3}
C = {A4, A5} => A ≠ C ≠ B