Important to remember that New Zealand is also a party to the https://en.m.wikipedia.org/wiki/Treaty_of_Rarotonga . For this question to resolve YES, besides repealing their local law, they'd also have to withdraw from the treaty or violate it.

Treaty of Rarotonga - Wikipedia

What if such an object enters their territory even though it is not allowed?

@Yev Nope. Must be allowed.

Anyone know whether fusion reactors are currently prohibited? Unsure how to resolve in that case.

@IsaacKing From the above Wikipedia article, second paragraph:
The nuclear-free zone Act does not prohibit nuclear power plants, nuclear research facilities, the use of radioactive isotopes, or other land-based nuclear activities.[6]

@NcyRocks Interesting. That directly contradicts the first paragraph right before it.

Under the New Zealand Nuclear Free Zone, Disarmament, and Arms Control Act 1987,[1][2] territorial sea, land and airspace of New Zealand became nuclear-free zones.

Yeah, it's a common misconception that New Zealand's definition of 'nuclear-free' thing includes power stations, but it doesn't. It does include nuclear-powered ships.

It's pretty clear-cut if you read the Act itself here (sections 5-7).

@IsaacKing That said, I don't see one being built any time soon.

@NcyRocks Thanks. I'll go ahead and include fusion power plants, and I've clarified the description that I care about what actually gets built or moved, not just allowed.

@NcyRocks I reckon most NZ voters would be surprised to learn that, and not in a good way

@IsaacKing "will nuclear power plants still be nuclear-free in 2032?"