That is only if you move to New York and do not report you are there. There is an exception for “just visiting”. I do not know how long it is. I am dual registered in Pa and NY. Once you register in NY you cannot break your registering duties simply by moving out of state. Since I moved back to PA in 2015, I am stuck registering in both states.
No state can ban you from visiting or traveling through their state. Might be only a few days, but they have to alllow you to visit.