> Does NZ still ban US warships from making port calls if the ships are nuclear powered?
Yes and no. For better or for worse, New Zealand does not favor nuclear power of any description. So all nuclear weapons-capable vessels, and all nuclear powered vessels, are prohibited from NZ waters -- not just US vessels.
So, if the vessel is Chinese or French or Martian -- it does not matter: if it is nuclear powered or nuclear weapons-capable, it must not enter NZ waters.
In practical terms, this has meant that the US Navy does not visit New Zealand. Not because they are not welcome: they most certainly are: providing their vessels are not carrying nuclear weaponry nor are powered by nuclear power.
The US Navy does not, as a matter of policy, confirm or deny whether their vessels are nuclear-powered or nuclear-weapons-capable. So, as a practical outcome, UN Navy vessels do not visit.
Not everybody in New Zealand agrees with this particular anti-nuclear stance: I certainly don't. Nuclear fission is a perfectly clean way to power modern naval vessels: much safer than diesel from an environmental-impact viewpoint.
In the same way that modern nuclear reactors are a reasonably good way to generate lots of electricity. Instead, we will use coal and hydroelectric power. And, as a result, pay $600 per month for electricity over the winter periods. Again, not everybody in New Zealand agrees with this stance: again, I certainly don't.