That is incorrect. Malcolm X on a few occasions thought that certain actions orchestrated under King, such as the Children Crusade, were too radical, saying men don’t put their children in danger.
And again, King was called a Communist in his own time. Some in the movement also condemned King for including Bayard Rustin, who was gay. His wife Coretta who go on to be a champion of LGBTQ+ rights in his name.
Both King and X had the same views on self-defense and guns which if they were white, would be considered “conservative.” But because they both believed in self-defense because historically (and now) black people had little legal protection, they are both considered “leftist,” as you say.