The central ideological conflict between The X Men and the Brotherhood of Mutants is arguably “should we protect or punish those that hate us?” That conflict, as well as the characters of Charles Xavier and Erik Lensherr, were all taken from the Civil Rights movement and the major figures behind it.
The basic foundation is the same: both MLK and Malcom X wanted the same thing (a nation where black people are accepted equal members of society) but were completely different in their approaches. While MLK spoke on the words of Ghandi and urged peace and integration, Malcom X believed hate for white Americans needed to be spread to counter the hate against the African Americans.
In the same model is Professor X and Magneto. Both wanted a world where mutants were accepted members of society living without fear of persecution. Charles Xavier believed the only way to live peacefully was to show that mutants are humans just like any others, and to resist violence because of its potential to widen the social gap between mutants and non mutants. Erik Lensherr, however, had no desire to be controlled by humans. He believed that the only way to gain acceptance was to fight human aggressors with a show of power. His main idea behind it was that there was no reason to suffer abuse when the power of mutants could put an immediate end to hatred directed against them.