This came up on Twitter yesterday after Margaret Mutu's comments, and while I love Twitter, the format is not good for serious discussions and explanations like this. A couple of people were curious so I'm going to expand on what I was saying to make it a bit clearer.
First off, I'm no expert on this. I'm white, I don't have to live with it, this is stuff I've learned from reading and speaking with people who do. Specific to New Zealand your best bet is to ask a Maori person (or other POC but Maori and Pacific Islanders tend to be the worst off, particularly Maori) if they'd mind explaining to you the slightly more subtle ways they experience discrimination, and not argue with them if they say no or you don't like what they say.
The problem with discussions like this is that there is more than one definition of racism. It means hugely different things to different people, where some think of it as only deliberate acts of hatred and others think of it as a wider system of unconscious values and ideals that works to disadvantage particular populations. The definition I use is one that was explained to me which is a sociological, academic concept of racism as POWER + PREJUDICE. A brown person can hate a white person or a Chinese person and a Japanese person living in a Western country (where neither of them have power) can hate each other, but they are not the socially advantaged group, so it's racial prejudice on an individual level rather than the usually far more damaging institutional kind.
Now, when I talk about power, this doesn't mean that everyone in that group is going to be well off. White people can be poor and marginalised. A white, mentally ill woman who's a sex worker and single mother is not going to be a very celebrated person - but she will be better regarded than a Maori mentally ill woman who's a sex worker and single mother. That's the key, that two people in the same situation have different possible outcomes solely due to their (perceived) race. And when I talk about institutionalised, that means it's not all deliberate actions by bigoted people. For example, in the US you'll get a different sentence for crack cocaine and powder cocaine, despite the fact that they're essentially exactly the same thing, because crack cocaine was viewed as more harmful and more addictive (a later study found that they have about the same level of addictiveness, among other things). Originally, the ratio was 100:1, with a mandatory minimum sentence of five years for possession of crack. Incidentally, crack users are more likely to be black. Obviously the result is a law that adds to the incredibly disproportionate numbers of black people in prisons. And even within that framework blacks are more heavily targeted - a 1995 study identified users as 52% white and 38% black, but those charged with crimes related to the use of crack were 88% black and 4% white.
Putting black people in prison was not the goal of the original law (probably), which means that by the strictest definition it wouldn't be racist. But the idea that crack is more harmful could have been influenced by unconscious racial views towards the black users of crack, and even if it was all a complete coincidence, it still had a terrible effect on the black population which would fall into the broader definition of racism.
A site I really like is Micro Aggressions. It's a tumblr that has dozens and dozens of tiny little stories, some of them only a couple of sentences, submitted by people who are marginalised. If you read one, it's rarely a "big deal". But the point is that there isn't just one. There's a lot of them. They're things that happen all the time, and that's really draining (speaking as a mentally ill queer person perceived as female, here). So when you live in a society where policy and law inadvertently discriminate against you and where the majority population* doesn't value or understand you, there isn't necessarily any recourse, because if you complain about something, the person with power has no idea of the context. They don't see the micro aggressions that the discriminated against person does. While I've learned from books and essays and blogs and conversations a lot of the ways racism operates towards Maori in New Zealand, I can't fully understand it because I'm still missing most of the picture.
What I do know, though, is that I'm unwilling to condemn a Maori woman for expressing reserve about white immigrants. I think that quotas won't work because the prejudices are already ingrained here too strongly, but I'm not going to argue with her basic premise, and I'm not going to pretend that her attitude damages me, because she lacks the institutionalised power to impact on my life in any way whatsoever. Let's face it - there's a reason she feels that way. Expecting POC not to feel that way is, frankly, a little irrational, considering everything.