This is a question about the nature of God. It basically suggests that for God to be literally omnipotent involves a logical contradiction. Schaefer agrees:
God is omnipotent. But omnipotence does not mean that God can do literally everything.... so God is not omnipotent. QED.
Being limited only by logical consistency is not all that much of a restriction.
The trouble is that once you start thinking that God is limited in any way it opens the door to other limitations. For instance: since the laws of logic are also created by God as part of creating the Universe, then this is like saying that God is restricted by His own Laws within Creation. (If the Laws of God are extensions of God's nature, then this is just to say that God can only act like God.) But this means that God cannot do anything supernatural. There are lots of Christians who will have issues with this. It means you cannot have a literal virgin birth or a literal resurrection.
Of course we can just say that God mostly obeys His own Laws, but may break them when it is important - then look to the Bible for examples. This misses the point: limiting God even a little bit opens this sort of can of worms in all kinds of areas.
Theists are better off asserting that, yes, God can create logical contradictions. Whether or not God does create such things is another question.