One of the sites I visited (via a recommendation from Jon Formet) suggested the following way out for multiverse believers:
There may be an infinite number of universes, and there may be at least one universe where you are a genocidal maniac, but if there is such a thing as moral behavior, and you are born as a moral creature, then on average you will be a moral person in ALL universes.
So someone like Hitler would be quite a mean fellow in most of the universes that housed him, while Mother Theresa would be quite saintly in most of the universes that housed her.
Thus your other selves could still have free will and make true choices in all the other parallel universes, and each of your parallel selves would have to face the same music at the end of time.
Thus when you feel only slightly tempted to do something, then you probably don't do that in very many of the parallel universes, but when you are sorely tempted to do something, even if you evade giving in in this universe, you probably give in a larger number of parallel universes.
I can almost accept this, but I still think it is more complicated than it need be.