What an absurd idea! I never realized how many people held to this idea until my wife and I had a child with a ... "birth defect." People I thought cared about us let us know that such things happen when you don't "live for the Lord." It's a disgusting belief. If these people ever read their Bible, they would know that even Jesus thought it was a stupid belief.
When his disciples asked Jesus if a blind man's parents had sinned to cause their child to be blind, Jesus response was:
"Neither hath this man sinned, nor his parents: but that the works of God should be made manifest in him." (John 9)
And maybe a "what is wrong with you????" (I added that in). God may have allowed someone to be born blind, but it had nothing to do with anyone doing anything wrong. Sometimes these things happen. We live in a world that falls apart. Bad things happen. You might wash a pair of pants with $100 in them. Genetic code might get mangled from natural processes. None of that means that God looked down from heaven, and saw me picking my nose in the car, and thought to himself:
"Oh dear, how should punish him for that? I know! I'll let his kid be born split in half! That'll learn him a lesson!"
The Old Testament is no excuse for such a insanely depressing belief either, because, again God said,
The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him.
So no. My child is not some crazy punishment from God for my "evil doings." Evil doings which usually, in the context of the conversation, consist of following Jesus teachings (imagine that! I'm evil for following Jesus teachings. The person they claim to follow). But that's another can of worms.