This is a complicated question that assumes that there is a single thread tying all these events. I'll just cover in my answer the US (limited) reaction to the 1974 Indian nuclear test, as it's interesting [to me at least] and also fairly obscure.
Nixon generally played little attention to nuclear non-proliferation, at one point declaring that "the Non-Proliferation Treaty has nothing to do with the security of the United States of America."
He also made the secret Nixon–Meir deal. He even dissuaded Japan from entering the NPT. Regarding the US reaction to the 1974 test (as the linked paper says):
The State Department’s first inclination was to criticize the test, but Kissinger disagreed, choosing a milder wording for the official reaction to the event. [...] The relatively mild criticism has been attributed to Kissinger’s aversion to ‘giving the Indian program an elevated status’, as well as the American desire not to draw attention to the impending US deal to supply nuclear reactors to Israel and Egypt.
The tame US response drew some private consternation from its allies, e.g. one British diplomat privately, but openly asked Kissinger in July 1974 ‘Is the NPT dead?’. Also
Kissinger also came under pressure from Congress for a change in
tack. Prominent senators spoke out after the Indian nuclear test to
express consternation at the administration’s non-proliferation policy.
After Ford replaced Nixon (and in fact while Nixon was on his way out in late 1974), Kissinger shifted gears and (following the 2014 release of some secret documents detailing the negotiations around NSG) he is now seen as a major promoter of the NSG... even though Kissinger (like Nixon) barely mentioned non-proliferation in their memoirs.
Even then, Kissinger was afraid that coming out in a strongly worded US condemnation instead of (first) securing the cooperation of major suppliers would be a bad strategy:
conference, Kissinger argued, would ensure that it did not ‘look like the
United States attempting to impose non-proliferation on the rest of the
world as a unilateral move’. [quoting form a 2 August 1974 meeting's minutes]
As further counterpoint (that the US was just favoring India) during this period, the Nixon administration was also at odds with the US public opinion and even Congress over the 1971 Bangladesh crisis (that turned into a war); the administration wanted to help Pakistan more, but the US public reaction to the refugee crisis, which found echoes in Congress, made it difficult for Nixon and Kissinger to pursue their strategy. Nixon was favoring Pakistan in no small part because it was the conduit of his overtures towards China, and hoped that showing solidarity with Pakistan would encourage China to respond favorably, because such a response would give some assurances to China that the US might do the same in the case of a China-Soviet conflict.
In the Indian perception, the U.S.-Pakistan-Chinese alignment that
emerged during the Bangladesh crisis was designed to interject superpower
influences into South Asia for the purpose of thwarting Indian
aspirations in the Subcontinent. The decision to send a task force into
the Bay of Bengal-headed by the nuclear-powered aircraft carrier Enterprise,
which many Indians believed had nuclear weapons aboard represented
the first threat by the United States to use military force
against India. As the discussions of the defense budget in the Indian
parliament in 1972 attest, this action greatly intensified the Indian debate
on the nuclear issue and increased pressures for the development
of a military nuclear capability. Proponents of nuclear weapons for
India repeatedly pointed to the American carrier as the reason such a
capability was needed. They advanced the argument, suggested by Indian
defense analyst K. Subrahmanyam, that "had India possessed
nuclear weapons the Enterprise would not have steamed into the Bay
of Bengal during the Indian-Pakistan war in what appeared from New
Delhi to constitute atomic gunboat diplomacy." India might have
gone nuclear in any event but the Nixon administration's tilt toward
Pakistan, including the decision to deploy the Enterprise, strengthened
the hands of the nuclear advocates.