There are certain things that love propels us to do. Whenever we find ourselves in a position to help we should not hold back from doing so. Giving and helping out those in need is one of the principles of Christianity that we should follow.
The act of love that was classified as the ultimate measure of love was that which had to do with giving.
John 15:13 KJV
Greater love hath no man than this, that a man lay down his life for his friends.
Christ was willing to lay down His life, His whole being for the sake of humanity. He knew that the only way to save man was to give Himself up. If we are opportune to save a life make ourselves available. A good heart would make us know that if we are in a position because of us someone with a health challenge would not die but live we should be there for them.
If Christ didn't hesitate to give up His whole body and its members, then I don't think there's a problem giving to people some parts of our bodies so that they can be able to live. Where God is upset us when we use our bodies to do evil. Donating an organ to save a life is not evil.