Reading the wiki page on motivations of the U.S for the 1953 coup. It says historians are not decided and then gives two examples.
Ervand Abrahamian says is was about oil, that Iranian nationalization would set a bad precedent and threaten U.S. economic interests. He gives a response by the secretary of state to Eisenhower as evidense that the threat of communism was just a "smoke screen"
The rest (and majority) is summarizing Gasiorowski. That this was right after they had "lost China" and fought in Korea, fear of Communist expansion was at a high point. That the U.S. looked at the Oil in Iran as something the Soviets must not get their hands on, regardless of legitimate that fear is in hind sight.
link to wiki - https://en.wikipedia.org/wiki/1953_Iranian_coup_d%27%C3%A9tat#United_States_motives
It's the combination, best described as "Fear of the oil falling into Communist hands."
Eisenhower and the Dulles brothers were under no illusions that Mossadeq was a communist. However, they feared he underestimated communist influence in Iran and would foolishly move Iran towards the Soviet Union as a means to maintain his hold on the country.
Keep some things in mind about the Eisenhower administration at this point: 1) They're plotting a coup in Guatemala, not because of a fruit company, but because they believe to their core that Arbenz is a communist and destabilising the region. 2) They're actually planning on overthrowing Syngman Rhee if he didn't stop threatening to renew hostilities in Korea (Nixon's trip to South Korea was effectively Rhee's last chance before the operation started moving). And 3) Eisenhower had a contradicting belief both that Britain and France should end their colonial empires, but should still maintain security in the regions those empires had been.
I presume most of the relevant NSC meetings are available in FRUS but the basic narrative that is presented by most writers, and indeed some historians, sacrifices a great deal for the sake of a consistent narrative. The fact is that while the plotting of the coup was always a kind of on going, stumbling sideshow, Eisenhower, Foster and Allen Dulles openly struggled with whether a coup was necessary to secure Iran, because that was the goal: keeping Iran secure, stable, and out of the Soviets' hands.
Even when the coup was occurring, and it looked like it might fall apart, Walter Bedell Smith cabled Eisenhower and said "We now have to take a whole new look at the Iranian situation and probably have to snuggle up to Mosadeq [sic]…I daresay this means a little added difficulty with the British."
But as for whether historians are "decided" that rarely happens. Take the Guatemalan coup for example. Many historians looking at diplomacy more from an economic side still argue that United Fruit was the main reason Arbenz was overthrown, and almost all journalists and "pop" writers make that case, partially because it moves more copies to portray U.S. foreign policy as a predatory corporate-driven machine. I'm not trying to go in to a whole other topic, my point is just that at the end of the day there is usually evidence for whatever position you like, it's just that some people only accept evidence for that position - which causes problems.
Sources: For the memo from Beetle to Ike - Memorandum for the President, August 18, 1953, Iran 1953 through 59 (8), Box 32, International Series, Ann Whitman File, DDEL.
"Mohammad Mosaddeq and the 1953 Coup in Iran" Edited by Mark Gasiorowski and Malcolm Byrne, (Syracuse: Syracuse Press, 2004).
And on the other end...
Stephen Kinzer, All the Shah's Men. The Brothers.
(I can provide more sources but OP has generally described the two dominant views of the coup among most).
Gasiorowski is highly reliable but fear of communism was not the reason, the oil was. The previous US administration was not getting involved so the Brits came up with the idea to promote the anti Community angle to sell the idea of the coup to the new US president. Iran unlike China had no real domestic communist movement, the Tudeh (Communist) Party of Iran was not a popular threat...or armed as in China. The fear of Communism was cooked-up and not just to sell the Iran coup. Back then the fear of communism was very useful. The US national highway system for example was justified and financed as an anti-Communist action, and rock n roll critics called it Communist too.
In the case of Iran the CIA had to manufacture a communist threat, going as far to bomb a prominent clerics house to blame it on "communists" in order to cleave Mossadeghs religious supporters away from him. The CIA smeared Mossadeghs not just a communist but also a homosexual and a Bahai too.