Some may argue that it is not moral to grow human organs at all, let alone test on them. This level of playing God seems to be too futuristic to be comprehended as a current possibility.
I have grown up seeing science progress to the point of cloning sheep and growing ears on the back of mice. This has never sat well with me personally, yet I never heard many people opposing it. I have, however, heard a lot about people opposing stem cell research in recent years. I think it’s safe to say that humans put a much higher value on their own species than they do on the lives of other species.