You are misusing the term "accept". And, for this reason, you are merely describing acceptance of possibility.
Hmm, yes I am describing the acceptance of a possibility.
But I do not think this is a misuse of the term. I am using the term as it is used in classical logic. I am simply combining the acceptance or rejection of two propositions to describe a position.
I understand that in logic we would say
If God exists, then God cannot not exist.
But this is secondary.
First we say assume God exists.
If God exists, then God cannot not exist (by non contradiction)
Likewise we say
Assume God does not exist,
if God does not exist, then God cannot exist (by non contradiction).
However if I say
assume God exists
Assume God does not exist
If God exists God cannot not exist (non contradiction)and
if God does not exist Then God cannot exist ( non contradiction).
So, one of these assumptions is wrong.
I have broken no law.
We can assume both, classical logic only leads to the conclusion that one is wrong. Therefore nothing in classical logic is contradicted by the belief in both.
However, your position becomes even more precarious when we acknowledge that other systems of logic exist.
And people can in those systems believe contradictory things. What is more, many physicists believe that two states that are mutually exclusive can exist at once. This is because some believe that multiple states coexist prior to observation.
Now, that people do in fact believe in mutually exclusive states illustrates your notions of impossibility are wrong.
But, what is more, that people can believe wrongly proves your position is wrong.
And finally, that one can rightly believe that one of their beliefs is wrong, provides an example of how this concept is not at odds with believing mutually exclusive propositions is not at odds with classical logic.