In the ninteenth century, the years after the initial waves of settlers arrived, there were large numbers of European settlers who lived, if not with Māori, then in close proximity. In Pukekohe, a region about 40km south of Auckland, there was a valley that had a Māori village at one end, and a settler village at the other. Many Europeans spoke te reo, the Māori language, and there was of course the Treaty, Te Tiriti o Waitangi, which had been signed in 1840.

Despite all these factors, Māori were not viewed as equals to white New Zealanders. Māori men could vote about a decade before white men got suffrage, but could only vote for designated seats, curbing their power at the polls. Māori were thought to be a dying race, and white New Zealanders considered themselves to be their natural successors as owners of New Zealand. Māori culture was largely seen as inferior and savage, similar to many indigenous cultures around the world. This continued through the 20th century.

During the 1960s, Māori had been under a policy of assimilation by the government. This wasn't a new policy, just the latest iteration of it. Schemes like the Hunn Report, that aimed at urbanising Māori and assimilating them into Pākehā society were utilised by the government, and involved methods such as housing Māori in white neighbourhoods, so that they would only have white neighbours and influences. This began to change somewhat during the 70s. An earlier, now deleted, comment pointed out that Māori had signed te Tiriti with the Crown, which would protect their land (it didn't), their chieftainship (it didn't), and their taonga (valuable items, whether they be physical or abstract like culture - it didn't). In 1975 however, the Waitangi Tribunal was established, and this changed the position of the treaty from a piece of paper in the past, to a more serious document. The Tribunal began to hear claims by Māori alleging Crown violations of the Treaty. At the same time, there was what has been termed a 'Māori renaissance', where efforts to revive Māori culture were made by Māori, which also persuaded the government to make some effort to do so. The idea was to promote Māori culture as being a vital part of New Zealand culture, and not something that could be lost. At the time, te reo was a threatened language, as many Māori had been beaten or disciplined in school for speaking the language, and as a consequence, refused to speak it with their children, allowing them to grow up monolingual. A big part of this was reconnecting urban Māori with their culture, which many felt disconnected from after the urban migrations.

The Māori renaissance felt influences from America, where the Civil Rights Movement had made advances for African Americans, and where the Black Panthers had pushed for pride in black culture. Māori had the same goals: to be allowed to have their culture be an acceptable part of their lives in mainstream New Zealand. To this end, schools were set up that educated children in Māori language only, full immersion. The activist group Ngā Tamatoa pushed for equal treatment of Māori by state services. In one of their more famous incidents, they broke up a 'haka party' at the University of Auckland. It was a tradition where the Engineering students would dress in black face, and perform a mock haka after graduation. In the late 70s, Bastion Point was occupied by Māori activists for over a year, in protest of the theft of Māori land there. This period featured large amounts of Māori activism, and a growing recognition that Māori had not been respected by the terms of the treaty. This was backed up by Tribunal rulings granting compensation to Māori for stolen land, and enshrining in law the value of te reo Māori as a language of New Zealand.

I think this was the turning point for Māori culture being recognised and adopted on equal terms by Pākehā. It happened gradually, and there's a long way to go, but the cornerstone of culture is language, and te reo Māori is more prevalent in New Zealand today, and there have been growing pushes for it to become compulsory in schools, and for people out of school to learn it. That acceptance of the language has made the culture as a whole more accessible to outsiders, and has helped a lot of Māori who live outside of their ancestral regions to connect with their identities and culture. Another aspect of this would be ta moko, the facial tattoos that most Māori used to have in the pre-colonial period. Moko represented your familial connections, and your ancestral history, and was an important identifier. While some people today don't like moko, it's become less of a stigma for Māori to have it, although not by much (facial tattoos having a lot of connection with gangs, not just in New Zealand).

The example you used was the haka, which is a prevalent adoption of Māori culture today. Not all Māori agree with its use, and quite a few Pākehā think it degrades us as a country by harking back to savage rituals. For those who don't know, the haka is most commonly seen by international viewers at the rugby. It's a dance that was used as a challenge in warfare, but also as a welcome to visitors, and as an acknowledgement of someone's achievement or passing. But while today's renditions of the haka are energetic and have a lot of effort put into them, and are a meaningful performance for the team, that wasn't always the case. This video shows the All Blacks performing it through the years. The early versions are quite slack and limp, with no seriousness behind it. It's good example of cultural appropriation - no meaning was attached to it, it was entertainment only, and it was a mockery of the original template. For contrast to the early versions of it, consider that the original version of the haka they use was the creation of Te Rauparaha, a powerful and influential rangatira (chief) of his iwi. It doesn't really match up. This was the case for many aspects of Māori culture over the course of the nineteenth and most of the twentieth centuries. In the years following the Māori renaissance, the haka performed by the All Blacks changed from the half-hearted performance of old to a new one where the players understood the meaning of what they were partaking in. The change is often credited to the All Blacks of the 80s, in particular their captain Buck Shelford, a Māori player who didn't appreciate the way it was performed. From his tenure onwards, the haka has been led and performed properly.

TL;DR. Māori were denigrated and seen as inferior by Europeans, just like many other colonial spaces. The adoption of Māori culture, and the respect for it, is a more recent development, that originated in the work of Māori activists who fought to have Māori culture seen as something worth preserving, and for Māori to be treated on an equal level with Pākehā by the government. The result has been a resurgence in the language, which led to greater understanding and pride of Māori culture.