Our Creator hasn't changed. However our understanding of God and his love for us has changed thanks to the teachings of Jesus.
One must remember that the Bible is inspired of God but not written by God himself. The old testament has much value but it was written by men who had a limited understanding of God. How do we know that?
When we look at the requirements of the ancient God Jehovah and compare them to the requirements of Jesus, it's evident that their theologies are radically different. That's why Christians today do not follow the ancient laws of Israel. God did not change. But we have. The Pharisees who followed the laws of Jehovah, the God of Moses, thought they had 'the truth'. They were sure they knew God and what he required, but in fact they were mistaken.
One thing most Christians believe in though, is that God is love. God's love always comes first before rules. That's what Jesus taught. That's why he butted heads with the Pharisees so many times. However there were situations in which even the Pharisees bent the rules in order to be humane and help people. Luke 13:14-17
Get the facts. What does Jehovah, Jesus, and the Bible say about blood and blood transfusions? Consider these articles.