What do moderates think Jesus died for?

[Acrobat]

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, 

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

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

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

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. 

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

Well, here lies the rub. 

You have your own particular criteria of what constitutes as ignostic and as an atheist, than others, including those who label themselves ignostic. 

I reject your definition, and accept there's. Under that definition you're an atheist. I am not claiming something about your particular belief, but under what label they fall under. 

I am under no obligation to assume your definition is correct, and their's is wrong. Especially given that you seem confused yourself, by referring to yourself as both ignostic and an atheist in your profile. 

But here are others who use a definition of ignostic, where it's not mutually exclusive with atheist. 

http://damienmarieathope.com/2018/07/ign...on-of-god/

https://theethicalskeptic.com/tag/ignostic/

https://agnostic.com/post/11606/any-othe...ning-up-ig

From thus forward I will refer to you as the Ignostic Atheist Bucky Ball.