Creepers spawn all over my well-lit island. So do animals. Can I make creepers not spawn but the animals do?
Increasing the light level of your island should prevent hostile mob spawns while not hindering passive animal spawns. Hostile mobs only spawn if the light level is below 7; remember that a torch provides level 14 light and this decreases by one for every block away from the torch.
As for why creepers are still spawning, the obvious answer is that your island is not as well-lit as you thought. Perhaps there is a cave somewhere you overlooked, or a spot where 2 torches are a couple blocks too far apart.