William III was neither a fanatical protestant, nor a hater of Irish or even Irish catholics. He famously forbade his army to rape and plunder before the battle of the Boyne and when he came upon a British soldier who'd killed an Irish civilian and was robbing him, he had the soldier hanged on the spot for insubordination. William was indeed a smart man, but he could be very cold and calculating. There is every reason to assume he knew that the De Wit brothers would be met by a wild mob on their release from prison, yet he did nothing to prevent their subsequent lynching. In contrast, he seems to have had a passionate affair with his first counselor, Lord Bentinck, while at the same time having a reasonably good relationship with his wife. He is a fascinating and complicated character and he does not deserve to be reduced to a cartoon character by Irish protestant lore and legend.
As for the introduction of protestantism in England, I would argue that it is due to Henry VIII and political convenience, not William III and conviction. William fought for himself, his glory and a throne. He was a relaxed moderate when it came to religion, often to the frustration of the Whigs. As for the grating, self-centered and disloyal behaviour of James II, he acted in a long family tradition.
Peter