Frankly, I'm not sure a constitutional amendment receives approval from the State Legislature. The judge may or may not be overturned for now, but given the State's politics and the way the political winds are blowing, there is no question that the judiciary will impose this eventually, that is, within two to three years. At that point, I would say that the white flight of the muiddle class, which has been going on for some time, will become a tidal wave.
It only takes a simple majority in each chamber to send a NY state amendment to the voters but that would require 30 of 104 assembly democrats (with all 46 republicans) to vote in favor. I don't know enough about NY state politics to guess what the likelihood of passage might be.
In any case, if the state legislature and electorate wants to halt such rulings, they can certainly do so.