Is the New Zealand Labour Party fundamentaly a conservative party?

[Pericles]

No it's not, NZ Labour has consistently moved policy to the left in government though of course a lot of people (sometimes myself included) would like them to go further. It's clear that Labour MPs and party leaders have the same basic left-wing values as any other Anglosphere left-wing party.

I'm not sure how supporting the rights of indigenous people is a right-wing policy. The context of this is that in 1840 the British government signed the Treaty of Waitangi with the Maori, which promised them continued sovereignty over their land. The breach of this Treaty is a big reason why Maori have such worse social and economic outcomes than Pakeha/NZ Europeans, and so it's right that we apply the principles of the Treaty so we can start upholding our obligations under it. Plus, this has evolved to be a bipartisan consensus.

The NZ Labour Party has moved on from policies like a capital gains tax not because it doesn't believe in them, but because it is making that sacrifice to win elections. Having lost 3 consecutive elections before the u-turn and clearly underperformed in the 4th (2017) compared to how they would have done if they hadn't left themselves vulnerable to tax scaremongering, and given the polls were actually close in 2019, the u-turn was an obvious choice politically (policy wise it was regrettable). NZ Labour right now is doing so much better than other Anglosphere left-wing parties, so it looks right now like their approach is a good one. Plus, New Zealand doesn't have much of a mood for radical change or populism-most people are happy with the direction of the country (the polling data on this question is very different to countries like the US), satisfied with democracy, and New Zealand didn't get damaged much by the GFC. So politically, New Zealand is still fine with third way politics and in some ways stuck in the 2000s. This doesn't mean Labour is 'at heart' conservative. Jacinda Ardern explicitly said she believes in a capital gains tax when she pledged never to implement one due to public opinion, and Grant Robertson clearly was very passionate about undoing the 1991 Mother of All Budgets.

Meanwhile, Labour has moved economic policy to the left in many other important ways-such as raising the minimum wage, expanding sick leave, extending the bright-line to 10 years so there's a quasi-capital gains tax on investment properties, undoing the cuts to welfare benefits in the Mother of All Budgets, increasing the top income tax rate to 39% and now  instituting sector-wide Fair Pay Agreements so that trade union power increases and the effect of the Employment Contracts Act is reduced. As you'd expect, Labour has been bolder once they won a majority-both because they can worry less about losing the next election and because NZ First is no longer there stopping left-wing policies from getting a majority in Parliament.

The obvious and simple answer is that Labour is a left-wing party that has policies applied to the NZ context rather than theories based on what other countries experience, and they are political pragmatists that want to be electable and keep power.