So I've been reading "A Problem from Hell" by Samantha Powers, and in the part of the book regarding Cambodia, she talks about how the United States want to avoid hurting its relations with China. The reason for this was that it saw China as a potential Ally against the Soviet Union. At the time, she wrote, the Soviet Union was engaging in de-Stalinization, while China under Chairman Mao disfavored this movement.
While I can understand this causing tension between the Soviet Union and China, I am confused why this wouldn't cause the United States to seek out more friendly relationships with the Soviet Union to the detriment of China. To my understanding, a big part of de-Stalinization was the acceptance of peaceful coexistence with the free-market west, as opposed to hostilely challenging it. Why wouldn't the United States try to take advantage of this movement, and work more toward containing China? Was it just geopolitical momentum that kept the Soviet Union and United States in an antagonist relationship at this point? Why wouldn't the United States be more concerned about working towards allying with China during its peak communist era?
"De-stalinization", to the degree that it was ever pursued as a serious political strategy, was mostly something conducted by Nikita Khrushchev when he was First Secretary of the Communist Party (from 1953 to 1964), but noticeably after his "Secret Speech" to the 20th Congress of the Communist Party on 1956.
This was mostly part of the so-called "Khrushchev Thaw", where he undertook to reverse aspects of Stalin-era political repression and isolation. These noticeably included domestic policies like lightening (but not altogether lifting) censorship and mass pardoning of political prisoners (but not all of them). Khrushchev also talked up peaceful coexistence with other countries, and reached out in a number of international venues, and hosting foreign visitors to events on Soviet soil (probably the most famous example of this is Khrushchev's "Kitchen Debate" with then-Vice President Nixon at the 1959 American National Exhibition in Moscow.
However, this openness didn't have a one-to-one linear fit with the Cold War, and even while the domestic "thaw" continued there was a serious worsening of relations with the US, such as the U-2 shootdown and imprisonment of Francis Gary Powers in 1960, and the Cuban Missile Crisis in 1962. Khrushchev himself began to sour on allowing too much openness in the Soviet cultural sphere, and once he was removed from power in 1964 and replaced by Leonid Brezhnev, the Thaw and de-Stalinization largely ended (there wasn't exactly a re-Stalinization, mind you, but there was a definite message from the new leadership that reforms were over).
Now it's important to note that all of this is before the US established diplomatic relations with the People's Republic of China, which began with Kissinger visiting the country in 1971, and Nixon's visit the following year (a liason office was opened in 1973, and formal relations established in 1979). This outreach to China also occurred while the US engaged in detente with the USSR, including events like Nixon signing the Strategic Arms Limitation Treaty with Brezhnev in Moscow in 1972, and the Apollo-Soyuz joint mission and Helsinki Accords in 1975.
However, US-Soviet detente did not long survive Nixon's (or Ford's) presidency, and by the late 1970s relations between the two countries were rapidly worsening (to the point that with the Soviet invasion of Afghanistan in 1979 and the US boycott of the Moscow Olympics and a grain embargo relations hit a nadir).
So specifically around the Khmer Rouge, which was in power from 1975-1979, it's important to keep in mind that from the perspective of US international relations at the time, relations with China were very much on the up and up, and relations with the Soviet Union were worsening. Good relations with China were seen as useful counterweight for the US against the Soviet Union (the USSR and China had actually fought border clashes in 1969, and the Soviets stationed tens of thousands of troops on their border with China and in Mongolia). On top of this, it's also worth noting that Cambodia under the Khmer Rouge got involved in a war with Soviet-ally Vietnam in late 1978, which would lead to a full-scale Vietnamese invasion and overthrow of the Khmer Rouge regime, and which involved a Chinese border war with Vietnam in retaliation (as the Khmer Rouge was a PRC ally). I'm not the Southeast Asian history expert so apologies for rushing through that, but that's the basic gist.
Which gets us all back to - while there was an ideological component to the Cold War, it was not really as cut-and-dry as "the US was against whoever was the most communist". The Cold War was first and foremost a strategic and military issue with the Soviet Union, and various Presidents of the United States were willing to establish friendly relations or provide diplomatic or material support to communist countries that were opposed to or challenging the authority of the USSR, whether Tito's Yugoslavia in the late 1940s, Ceausescu's Romania in the early 1970s, or the PRC from 1971 on. The USSR softening its domestic and even international policies did not completely remove the real strategic and security dangers that the US government perceived to be arrayed against it, and China, even under the pro-Stalin Mao, was not considered to be remotely the same kind of threat, and seemed to be a possible counterweight to Soviet influence and power after the Sino-Soviet split.