I have no idea of the actual details, but from my far removed distance, I can tell you what it looks like.
It looks like legal NYC pistol owners are once again pawns in a bureaucratic pee-ing contest. It looks like someone in Nassau is ticked at NYC and is not honoring NYC permits as a means of expressing their ire. With the law abiding gun owner caught in the middle, again.
I grew up in NY state, during the 70s, moved away in 79. So my knowledge of NY law stopped being up to date about then, so you will have to check carefully to see what is, and is not current NY law.
When I lived there, and had a NY state pistol permit, it stated right on the permit that it was not valid in NYC. Everywhere else in the state, it was valid, but not in NYC. ONLY permits issued in NYC were valid in NYC. NYC permits were considered valid throughout the state, but NOT vice versa.
You'll have to check the current laws carefully. There may have been a change that allowed your situation to happen. OR, perhaps, there might not have been. I am guessing here, you need to check ALL applicable laws (and it might NOT be a gun law being used for the justification here), I can see a legal situation where the rest of NYS might not be required by law to honor NYC permits (maybe for any/everything), not just pistols.
The fact that the state always has honored NYC permits, might just be a courtesy, not a legal mandate. It might constitute the needed precedent if this becomes a court matter, but NYS (and it could be legally a county by county decision) might not be legally bound to honor NYC permits.
It might be that the fact that the State (through all its govts) has, since the implementation of the state permit system, generations ago, always honored NYC permits might just have been a policy, and not a legal requirement.
IF this is the case, and the Nassau Co. officials ARE on legal ground, then they do have the right to refuse you. Contact your local guns rights groups, NYC and NYS! see if they are aware this is going on, and if so, what their stance is, and go from there.
With the limited information I have, these are the possibilities I see, in no particular order,
1) The refusal to accept your permit may be the actions of a "rogue" official, acting on their own, and against the law/policy precedents.
2) The refusal is sanctioned, official Nassau county policy.
It has to be one or the other. Which one determines the next effective step to be taken.
IF it is official, legal policy, it may be deliberately directed at gun owners (and in NY, that's always possible), or it may be feuding bureaucrats using gun owners as pawns or catspaws in some other disagreement, simply because they have the power to do so.
You need to find out (and make others aware) to determine what you/we can do about it. Until then, your only option is to obey the law, all of it, while working to get things fixed.