Those 2 things are the polar opposites, and agnostic theist an oxymoron
Expecting people to operate in a purely logic driven manner is a great road to disappointment, and one could argue that it also reveals a deep lack in understanding of your own self. People are not logical beings.
Life is not debate club. You can insist all you want that it's not a logically compatible "belief system" (or however you want to label it). You can argue that there should be a different, more etymologically sound name for it.
But regardless of your objections, agnostic theists do exist, and "correct" or not that is what they are called.
Edit: I'm not even one of them, I just absolutely loathe this sort of behavior online, especially when discussions of theism and belief systems come up.