Actually very few (if any) theists and a minority of atheists have any idea of the basic concepts of logic and do not have a logical basis for their view.
I can assure you that some theists do have an idea of the basic concepts of logic.
The Paradox of the Stone is not a matter of improper definitions and assumptions but rather of sloppy proof technique. If approached rigorously, the “paradox” disappears and no contradiction presents.