My first thought (as I indicated in an earlier post) is what happens when they move out of NY and say, try to get a drivers license in another state? They'll be laughed out of the DMV. Then.... they go find a sympathetic lawyer to sue the state for denying them a license to drive, and all kinds of cans of worms get opened.
No state will ever recognize their altered Birth Certificate.
(Well, maybe Vermont and California)
But it might be decided that the Constitution requires states to honor it. Maybe we need a Constitutional amendment that allows us to eject states from the union.