In which states is it not required to register a birth, or if it is
required in all states, in which states is the penalty for refusing to
register the lowest.

Assume that the parents will refuse to provide any information
whatsoever regarding the birth of their children, which will done in
private, and are willing to face whatever penalties need apply, if
any, what state would be the best to have children in if the intent
was to insure that no legal record whatsoever of their birth was
generated?

A satisfactory answer will either list the states where their is no
penalty for refusal to register a birth, or if there are no such
states, will list the state(s) with the lowest penalty.