You will naturally get a fair bit of variance to opinions on this from us Kiwis, so rather than replying to any of the poster's below I figured i'd just add my own two cents separately. You're essentially asking for the vibe, not the truth - and realistically your own experience is going to be the most valuable way to determine what it is like for you.
NZ doesn't have any out & out fascistic parties anywhere close to political power, but there are still right, and far-right political ideas prevalent in our discourse along with other pet issues that would not be misplaced amongst most other alt-right movements worldwide.
Many Pākehā will argue against this - but my contention is that from most measures NZ is a fairly racist country. Naturally, given it was a colonised country, this is particularly noticeable against Māori, but it also impacts Polynesian people, and to a lesser extent also to Asian, Latin and African peoples.
The 3 right-wing parties in / close to parliament all use dog-whistle style politics to gain support by attacking initiatives that would attempt to redress the imbalance in social outcomes - health, education, justice etc. Some parties bring out that rhetoric most loudly come election time (NZ First), but the two elected parties (National, Act) do it so casually that it sometimes gets missed how much they use it as a crutch to solidify their support base.
Many of the other pet issues for the alt-right are thankfully still fairly niche here. Though the anti-trans as a gateway to anti-LGBTQ is getting stirred up as well. A lot of extra stuff kicked off around the covid-19 pandemic, and there's a lot of misinformation, disinformation and people peddling bulls%&t to suckers for money.
Mostly this initially comes in from foreign grifters or religious fundamentalists which is to be expected I guess, but eventually we seem to produce local versions of the same. Supporting that effort there is also a group co-opting free speech movements as a basis for importing more alt-right, far-right and fascist speech into regular discourse. That's a complicated movement as some people involved probably are genuinely in support of free speech as an ideal, but its certain that others use it the same way all fascists do.
I think that's a reasonable snippet of the cultural far-right politics here, but probably another thing to realise is that New Zealand has had a neo-liberal economic consensus since the mid-late 80s. This means that economically our "centre" is actually right wing. Low tax, low government intervention, small government in terms of GDP, selling off of state assets, lots of user pays style things, minimal support for those unable to work etc.
To be sure there's loud arguments that Labour^1^ are socialist commies, all about traditional big government etc, but really them and National^2^ are economically two sides to the same coin. Particularly as neither will do anything to increase taxes on the wealthy, neither will do anything significant to address inequality, or improve housing affordability or have policies that will actually allow the country to reach pollution related targets etc.
^1^ nominally centre-left, but IMHO more centre-right thanks to the left splitting off from them after the neo-liberal reforms of the 80s, eventually mostly coalescing into the Greens
^2^ nominally centre-right, but IMHO they're 3 parties smudged into 1, centre-right, religious fundamentalist and far-right