A good starting point would be this answer I wrote about the US and anti-communism in the Cold War - namely, that while "anti-communism" might have made good press, it's really better to understand the US position as anti-Soviet. It was more than willing to deepen ties and provide material and even military assistance to communist regimes and movements that found themselves at odds with the Soviets or Soviet bloc.

In the case of US-China relations, the move from hostility to cooperation was very much because of Cold War geopolitics. The Soviets and Chinese had begun to drift apart with Khrushchev's denunciation of Stalin in 1956 (Mao considered this treachery). In 1960 the PRC denounced the USSR as "revisionist", and the Soviets responded by withdrawing thousands of Soviet advisors from the country and largely ending its aid (the PRC was the single biggest recipient of Soviet foreign aid in the Cold War era). By the late 1960s the Sino-Soviet split had advanced to the point that the border was heavily militarized and war threatened - border clashes actually broke out in 1969. So the Soviets and Chinese at best viewed each other as competitors around 1970, and this was at a time when the Nixon administration was attempting to reshape US international relations.

While the US was pursuing detente with the Soviet Union, it also sought to reach out to the PRC as a counterweight to the USSR. Relations started with Secretary of State Henry Kissinger's secret visit to China in 1971, and then with President Richard Nixon's very public visit the following year, but continued with informal diplomatic relations throughout the 1970s, culminating in US diplomatic recognition of the PRC and the establishment of formal relations in 1979. Formal relations would lead to military ties, amounting to billions of dollars of US arms sales until Tiananmen Square-related sanctions in 1989.

As for how Vietnam and Cambodia fit into these equations, I can give a brief overview, but I can do nowhere near the justice to the topic that u/Shadowsofutopia does - you might want to start with one of their answers, but should also check out their podcast.

Very briefly - Vietnam after 1975 tended to gravitate more towards the USSR than to the PRC - partially this is from the long history of Chinese domination of Vietnam, and partially from Vietnamese treatment of its ethnic Chinese minority. The Khmer Rouge in contrast, despite also being communist, had major issues with Vietnam (as Khmer nationalists viewed "Lower Cambodia"/southern Vietnam to be historic Khmer territory conquered by Vietnam), and Khmer Rouge-led Democratic Kampuchea quickly found itself at war with the Socialist Republic of Vietnam by 1977. This ultimately led to a Vietnamese invasion of Cambodia as a whole and the installation of a friendly regime under Hun Sen (who is still the Prime Minister), with the PRC still recognizing Democratic Kampuchea (now fighting an insurgency) as the legitimate government.

So this is where the US comes in, ultimately taking a super Realpolitik position with regards to the USSR, especially as US-Soviet relations worsened after the Soviet invasion of Afghanistan in 1979. The US was essentially supporting the PRC (which was an anti-Soviet counterweight) by also supporting their Khmer Rouge allies, and in turn was opposing a proxy-of-a-Soviet-proxy, ie opposing the Hun Sen regime and the Soviet-allied Vietnamese occupation forces in Cambodia. Things eventually got to the point where the PRC and Vietnam themselves fought each other directly in the 1979 Sino-Vietnamese War. The Cold War alliance systems could get quite tangled and complicated indeed.