I am not sure what your point is. Surely it is sufficient to know that New Zealand (Aotearoa) was inhabited by Māori long before it was inhabited by Europeans. Therefore, I do not think that a European New Zealander has any business saying that a Māori woman should not serve as our foreign minister basically because she looks too much like a Māori. Māori culture is New Zealand culture. To say that Māori culture is “ugly” and “uncivilised” is itself ugly and uncivilised. Therefore, I do not see that the precise meaning of Ms Mahuta’s moko kauae makes any difference to anything.
As @JharekCarnelian has said, a large part of the interpretation of Māori tattoos is indeed to do with genealogy (whakapapa). When a man has his whole face tattooed, somebody who is sufficiently knowledgeable about Māori culture should be able to interpret details about his family, social status, and occupation. In the case of Ms Mahuta’s tattoo, it is specifically based on a design from the ridgepole of her ancestral meeting house. In fact, she has several other tattoos on her chest, back, shoulders, and feet. Her tattoos represent her father (Sir Robert Mahuta), her aunt (the Māori queen Dame Te Atairangikaahu), and her children.
My two nieces in New Zealand (who have three-quarters Māori ancestry) have beautiful moko kauae. My daughter (who has one-quarter Māori ancestry) is very enthusiastic about Māori culture, but has no plans to get moko kauae (although she does have other moko). Basically, she’s worried about permanently changing the appearance of her face, but she also worries about how a facial tattoo would be perceived outside New Zealand (she currently lives in the UK). She is a paediatrician, so when she mentioned this, I said that I was sure that her patients would think that she was pretty cool (or whatever they say these days). She said it wasn’t the children she’d be worried about! Interestingly, although it is strongly disapproved of for a non-Māori to have moko, the Māori deem anybody who has a Māori ancestor to be a Māori, so my daughter and her cousins are equally entitled to have moko kauae. As I am not in any way Māori, my own Māori tattoo is regarded as “kirituhi” rather than “moko”.