I disagree with the OP. See Jon Lee Anderson's work on Che and in it his account of the Cuban Revolution. It's by no means the final word on this subject, and it only briefly touches on class struggle, but it sheds some light on this.
The Cuban guerrillas began their socialist policies way back in the Sierra Maestra days, actually forming the beginnings of mass organisations with the peasants there. these were incipient soviet-like bodies in which peasants could discuss their problems and the ways to overcome them.
Before the war was over, Che and Castro were carefully integrating communist advisors into the guerrilla army. These advisors were instructed to not make their communist politics obvious, and to use local and national examples to make their point so as not to scare the people raised in a conservative catholic society away.
It's more important to study deeds than rhetoric. Castro was wisely pretending to support bourgeois democracy to get money from people who valued that. Just like there's left wing republicans I know who were active in trade unions and supported socialist states, yet presented themselves to their conservative American cousins as green catholic nationalists and 'play the green card' to get some donations out of em.
More to the point, though, the Cuban Revolution did begin as a bourgeois revolution, although many of its personnel were leftist. It was formally for bourgeois democratic rights.
In the process it was transformed into a leftist, mass struggle in which masses of workers took over their workplaces and laid the basis for socialism.
Lenin himself commented that revolts whcih begin as petit bourgeois nationalist struggles can eventually become proletarian socialist revolutions. One has to understand the dialectic of forces at work to grasp that reformist struggles can be taken over by the masses and transformed into revolutions.
to say that Fidel was not communist is more complex. What he seemed to disagree with most was not communism, but the dogmatic ideas most communists had about revolution. Fidel was stirring up strikes from his childhood, and spent his legal career defending the poorest in Cuba, this hardly seems like a Jeffersonian Democrat to me.