I'd have to imagine that the number of folks whose religion prohibits organ donation is so relatively minute that it probably does not pose a realistic factor in this discussion.
And this thread as convinced me that folks should have a say in what happens to their bodies after death. Think of it as a house. You're certainly not going to use it after your death, but of course everyone feels they have the right to dictate what happens to it after they die. Just because some homeless people may benefit from using your house when you're gone and not utilizing it anymore doesn't mean that's what should necessarily happen.
However, the Gov't (American gov't, anyways) has an "opt-out" program too. It's called a will. If you don't leave a legal document, the gov't can do all kinds of annoying, interfering, and value-reducing actions with your house.
An addendum question: Maybe the government should consider offering a tax credit for blood and organ donations? Now *that's* what I'm talking about!