I’ve heard it contended that Blessed John XXIII was actually a theological conservative and that is why it is puzzling that so many dissenters/liberals invoke his name, ie., “If we only had a pope like good Pope John,” and “if only he had lived.” The conjecture is that contraception would have been permitted, women priests, etc., but that those things would have never happened under Blessed John, due to his theological conservatism. His public face was due to the fact that he was a nice man and that he’d spent his public ministry as a Church diplomat (as opposed to the role held by Joseph Cardinal Ratzinger before he was elected Pope), but I suspect that he would be a bit startled at the stuff suggested by some Western Catholics in North America and Europe.