You have touched on an interesting issue there, Spooony. The myth that SA would not allow NZ to include Maori players. I found a few interesting pieces on the internet.
The first one is one that supports the myth in a way:
www.teara.govt.nz/en/nga-ropu-tautohetohe-maori-protest-movements/page-4
M?ori had long held concerns over sporting contacts with apartheid-era South Africa, but protests began in 1960. Prior to this New Zealand M?ori teams played against South Africa in 1921 and 1956. The problem to come was foreshadowed in the 1921 match played in Napier, when a South African journalist sent a telegram home regarding the match.
Bad enough having play team officially designated New Zealand Natives. Spectacle thousands Europeans frantically cheering on band of colored men to defeat members of own race was too much for Springboks, who frankly disgusted.1
1960 tour
In 1960 it was made clear that South Africa would not tolerate the selection of M?ori players for the All Blacks team to tour its country. The New Zealand Rugby Football Union (NZRFU) decided to send racially selected teams to South Africa. This was not the first time that M?ori players had been excluded, but it was the first time that a significant protest campaign was organised. A campaign emerged with the slogan ‘No Maoris, No Tour’. Anglican bishop Wiremu Panapa led a petition for equality between M?ori and P?keh? over not just the tour but wider instances of racism and inequality in New Zealand. The tour went ahead anyway.
In 1967 a tour of South Africa was cancelled because M?ori were still excluded.
Also from that piece:
In 1973 the government under Prime Minister Norman Kirk effectively forestalled planned protest actions when it intervened to cancel a planned Springbok tour of New Zealand, as the team was to be selected on grounds of race rather than merit. (Interesting to note that they were up in arms about players being selected/omitted based on race, yet today they do not have any issues with it at all)
The next pieces, however, refute the fact that SA did not allow Maoris but rather support the idea that NZ decided not to select Maoris in their squads:
www.teara.govt.nz/en/maori-rugby-whutupaoro/page-2
M?ori versus South Africa
In the 1920s the clash of race and rugby continued. In 1921 the South Africans toured New Zealand for the first time. Parekura Tureia got his chance to play the South Africans as he captained the M?ori All Blacks in Napier, a prospect that didn’t please some of the visiting Springboks. Following the game a cable was dispatched by South African journalist Charles Blackett that sparked an outrage. In it, Blackett commented that having to watch ‘thousands [of] Europeans frantically cheering on band of colored men to defeat members of own race was too much for Springboks, who frankly disgusted’.1 The Springboks won 9–8, although there was controversy over the refereeing.
M?ori players would be excluded from the 1928, 1949 and 1960 tours of South Africa. One result of this exclusion was that the New Zealand Rugby Football Union (NZRFU) became more open to allowing M?ori to assert a level of autonomy.
The same goes for this one:
'No Maoris - No Tour' poster, 1959
In May 1960 the All Blacks were due to leave for a tour of South Africa. They had finally won a series for the first time in 1956 and this was a much anticipated rematch between the two powerhouses of world rugby. However the 1960 tour is best remembered for the fact that no players of M?ori descent were selected. The decision to comply with South Africa’s strict segregationist apartheid policies by not selecting M?ori players caused outrage. Some of the biggest public protests in New Zealand’s history failed to convince the Labour government to intervene. Prime Minister Walter Nash supported the rugby union, arguing that to include M?ori ‘would be an act of the greatest folly and cruelty to the Maori race’.
The Citizens’ All Black Tour Association, of which Ng?i Tahu leader Frank Winter was a prominent member, campaigned to stop the tour, using the slogan ‘No Maoris – No Tour’. More than 150,000 New Zealanders signed a petition opposing the tour – this remains one of the largest petitions in our history. Others marched in the streets to voice their opposition. One unique form of protest came from the hugely popular Howard Morrison Quartet. Band member Gerry Merito transformed Lonnie Donegan’s ‘My old man's a dustman’ into ‘My old man’s an All Black’ to make a point about the decision to tour without M?ori.
Despite these protests the tour went ahead.
When the All Blacks toured South Africa in 1970, M?ori players were able to travel as ‘honorary whites’, a situation that appalled Winter and others in New Zealand’s growing anti-apartheid movement.
The Springboks played a New Zealand M?ori XV at Napier on the first tour in 1921, winning narrowly, 9–8. One South African journalist reported his shock at witnessing white supporters actively supporting the M?ori XV. The two teams next met in 1956, when New Zealand M?ori were defeated 37–0, and again in 1965 when they were defeated 9–3. Napier was the venue in 1981 for a hard-fought 12-all draw.
On the 1976 tour to South Africa the All Blacks played a South African Coloureds team in Cape Town, winning 25–3.
All-white All Blacks leave for South Africa
The slogan ‘No Maoris − No Tour’ fell on deaf ears as this controversial rugby tour went ahead. The issue of sporting ties with South Africa was eventually to split the country in devastating fashion in 1981.
Touring South Africa, with its entrenched racial segregation, had posed problems for New Zealand rugby since 1928, when the All Blacks first travelled there. Although M?ori players had always been eligible to represent New Zealand, the NZ Rugby Football Union chose not to select them for tours to South Africa. In 1928 this meant leaving players like the legendary George N?pia behind. No M?ori would be selected to tour South Africa until 1970, and even then they had to travel as ‘honorary whites’.
In 1960 nearly 160,000 people signed a petition − one of the largest in New Zealand history − opposing that year’s tour. They argued against the selection of what amounted to an ‘all white All Blacks’ team. Groups like the Citizens’ All Black Tour Association campaigned with the slogan, ‘No Maoris − No Tour’. Others argued that politics had no place in sport. In the end, the Wilson Whineray-led team left for South Africa as planned.
Meanwhile, the Howard Morrison Quartet had a big hit with the single, ‘My Old Man’s an All Black’, which took a dig at the decision to leave M?ori players out of the team:
Oh, my old man’s an All Black,
He wears the silver fern,
But his mates just couldn’t take him
So he’s out now for a turn.
(Fi Fi Fo Fum, there’s no Horis in this scrum.)
For the record, the All Blacks lost the controversial series 2–1, with one match drawn.
And then there is this from the NZ Govt Archives:
Controversy regarding the 1960 All Black tour
The decision to proceed with the 1960 All Black rugby tour to South Africa, while excluding Maori players, was one of the more controversial issues during Walter Nash's Prime Ministership. It brought to the fore the issue of rugby and race in New Zealand.
Previously, in 1948 there had been some protests against sending a rugby team without Maoris to play in South Africa. However, in 1959, when the Rugby Football Union proposed to send another all-white All Black team to play the Springboks the protests were bigger. A huge petition containing 153,000 signatures called for the abandonment of the tour.
However, despite Nash's opposition to apartheid and despite a lifetime of denouncing racism, Nash (along with his cabinet and caucus) decided not to intervene in the decision of the Rugby Union and the tour went ahead.
In April 1960 Nash defended the decision of the Rugby Union, saying 'it would be an act of the act of the greatest folly and cruelty to the Maori race to allow their representatives to visit a country where colour is considered to be a mark of inferiority'.
Here is a document on the Rugby Tour Deputation which also explains the government non-intervention stance. Interestingly, the National government seemed to take a similar view on the issue.
Archival reference: R22851171, folio 23