What do moderates think Jesus died for?

[Bucky Ball]

Yes it is.
They have already told you they accept that the notion of a deity is coherent, and you are agreeing/confirming their position with another label.
In order to be an "a-theist" there has to be something to "lack". Since there are no gods, and the concept is incoherent, there is nothing to lack.

In my hypothetical, the person who indicates he believes in God, is rejecting the label that he's a theist. He is wrong, because theism mean a belief in God/s, 

That's not what you said here, (or at least is not at all clear).

If someone came in here saying they believe in God, pointing out that this person is a theist isn't telling them what they are thinking

In order to be a-theist, you just have to lack a belief. 

Again, YOU don't get to tell anyone what they think. In order for ME to be an atheist, THEISM has to be a coherent and defined *thing*. It isn't.
Therefore one of the many possible positions in igtheism may be a category for some.

If you find a concept too incoherent to believe in, you lack a belief. 

There is nothing to lack as there is NO CONCEPT worth addressing.

Coherency might lead you to accept that belief or deem it as false, but it's not required to lack a belief in it. 

I neither accept the belief nor deem it as false ... there is nothing to lack. There is no value in a label or need to take any position with respect to complete nonsense.

If you ask me do I believe in xjoiuiuiur, I'd say I lack a belief in it, because I don't even know what the means. Knowing what it means might change this, but lacking knowledge of its meaning, leads me to lack a belief in in. 

That's nice. YOU get to do what you want. YOU do not get to tell others how and what they think.

the incoherency is justification for my lack of belief one way or the other.

Thank you for describing your thought process, which is valid FOR YOURSELF.