Are Theists Illogical for Believing in God?

[Purple Rabbit]

whatever alternatives should be feasible by logical means, right?

Not necessarily.

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

Then for everyone defining A as 'just logics' B would seem as adapted logic and C would seem illogic.
But for everyone defining C as 'just logics' A and B would seem illogic. So what is truth?

Consistency within a framework is no guarantee for consistency among frameworks.