It gets worse.
You'll notice the overt racism in the first cartoon. Two brown parents - either Maori or Pasifika - playing to a familiar script. Add an element of classism and fat shaming and you have a cartoon that "promotes discussion". Poverty isn't funny, though.
Race is a proxy for class. The cartoons recognise that and mix the two for maximum offense. Not in an ironic, making a deep social comment sort of way, but in crass play at the readers prejudice. Racism is magnified and normalised when it's presented in the media. In an ideal world the media would be better than that, but not the Malborough Express and the Christchurch Press.
The second cartoon isn't an overt play on race. However, the cartoon leads you that way - deliberately. The women are portrayed as unfeminine, a (mostly historical) way of demeaning brown and black women. The family is overweight, the father is pissed (in possibly a Once Were Warriors trope) and the mother is sucking a cancer stick. Ha, typical pohara maori behaviour. Not.
You could also read the "White Maori" slur into the cartoon as well. It's sad that these attitudes survive and find an outlet. Everyone is entitled to their views - even racist views - but not every view is entitled to equal weight. Running the cartoon is effectively an endorsement. In the wake of the Air New Zealand ta moko controversy, Maori aren't having a great week.