In 1996 new legislation was introduced to protect our native species and agricultural industry from unintentional threats aka bio-security. This means anything not growing in NZ before 1996 does not make the cut, and importation is next to impossible. This is controlled by the EPA with MPI responsible for endorsing it.
However, a recent addition to this list (and it took a lot of effort to prove it was growing before 1996) is Pleurotus ostreatus. But, even with its inclusion on the list no Mushroom grower in NZ has successfully been able to import it.
Fortunately, some of these can still be purchased frozen, canned or dried.
The "allowed" mushroom growing list
Here’s a list of exotic, edible fungi approved for import. Aka, what we are allowed to grow and buy fresh.