No, he was a Leftwinger. A Liberal who maybe agreed with some aspects of Marxism.
What most Conservative Americans don’t seem to understand about the Left is that there’s a long anti-Communist tradition among Western Liberals. Some of the most rabid anti-Communists of the postwar era were Liberals (ie George Orwell).
Based on Oswald’s writing and things he told people close to him after he returned to the US from the USSR, he wasn’t a Communist by that time and didn’t view the Soviet system as superior to the American political system. In the summer of 63’ he wrote that ‘he chose the LESSER evil by returning to the United States’.
He rejected Racial Segregation and supported the Civil Rights movement which put him in line with most Liberals in the early 60s. It also makes sense that he agreed with Kennedy’s support of MLK and Civil Rights.
When I look at Oswald’s biography, the biggest thing that sticks out for me are his numerous friends and associates who were rightwing or rabid anti-Comminists.
I can’t name any friends or associates of Oswald in the US who were Far-Left or communists. Isn’t that odd? The Paines are close to the only known Far-Left associates of Oswald and I suspect that they were Liberal anti-Communists.
As for his support of Cuba/Castro, I’m not certain that it was genuine or based on devotion to communism. Castro was still a darling of the Left in the early-60s. People on the Left were still optimistic that he might be a great leader for Cuba at that time.
Castro, when he visited Harlem in the early 1960s, called out the hypocrisy of the US in terms of the way Black Americans were treated. The contradictions were noted by Dr. Martin Luther King, who opposed imperialism and colonialism:
Cuba’s willingness to exploit the United States’s contradictory foreign policy position and domestic racial turmoil helped spur the White House to resort to terrorism and other illegal, covert reprisals against the island nation. It also reinforced the repressive instincts already being brought to bear against American blacks. Ten days after Martin Luther King, Jr. denounced the botched Bay of Pigs invasion as “a disservice … to the whole of humanity” and called on the United States to “join the revolution” against “colonialism, reactionary dictatorship, and systems of exploitation” the world over, the Senate convened a committee investigating Cuban influence on American blacks…
https://newrepublic.com/article/131793/castro-came-harlem
I tend to view Oswald and the JFK assassination within the broader context of what was happening in the US in those times. I don’t know if others do this.
Even if we accept at face value that Oswald was a devoted Marxist or Communist when he was a naïve teenager, we're faced with the question of why he returned to the US. Most likely he became disillusioned with Soviet style communism while living in the USSR and his remarks in 1963 where he ridiculed communists and the Soviet Union were genuine...