Each of these refutations assumes that all skeptics/agnostics/ignostics are the same in their degree of believing the basic idea of whatever particular system they espouse.
Not all skeptics are pyrhhonists, which by Socrates' demonstration are indeed contradictory.
Not all agnostics are radical to the extent of claiming absolute knowledge that they don't know, in fact most are just skeptics regarding God, they have certainty on other things more than likely.
And ignostics as well have at least two forms, if not at least a third, the third potentially being the group you have pointed out in some form of refutation. But technically ignosticism only says that in order for an adequate discussion about God, a coherent and falsifiable definition must first be presented. And if this is unable to be presented, they take a theological noncognitivist perspective, stating that the question is meaningless and has no real content within it.
Similarly, atheists do not take God as seriously as you would believe they consciously or subconsciously do, therefore they are not being contradictory in disbelieving in something that they recognize as having some significance but still not believing in it as reality in the same way all humans essentially recognize gravity for instance.