Of course we should have a provision for people with certain beliefs, standards, or certain medical conditions to opt out, as becoming an organ donor should always be a choice. However, I think a lot more people are willing to donate their organs than are signed up to do so, and making organ donation an opt-out program would give busy people the peace of mind that should anything happen to them, they will have the silver lining of saving others' lives.
Sadly enough, the inspiration for this idea came from Facebook, where every new change is vehemently fought, but eventually accepted, because they make it an opt-out, rather than an opt-in program. Most people who don't feel strongly about new Facebook initiatives don't bother to opt-out, and so the change is widespread. Think about how awesome it would be if most of the people in the nation were organ donors, rather than the other way around. Face recognition software is just scary though.