The novelist James Baldwin is quoted as stating: "The only time non-violence is admired is when the Negroes practice it."What does this quote mean...

I happen to disagree with Baldwin on this one.  I think he's being verbally ironic here, using tongue-and-cheek overstatement.

Gandhi was admired for his non-violence.  Thoreau too.  Jesus.  The Dalai Lama.  Cesar Chavez.  Leo Tolstoy.  Albert Einstein.

There were generally two schools of African-American Civil Rights in Baldwin's time: Martin Luther King and Malcolm X.  Both were essentially non-violent, although Malcolm X, I think, wanted a race war in the streets.  King's philosophy was descended from the non-violence of Christ (Christianity: "love your enemies," "turn the other cheek") and Gandhi (Eastern Philosophy: "just means lead to just ends").  X called for minority groups to arm themselves in preparation for a race war; he advocated forming "shotgun clubs" for self-defense, though not explicit violence.

It is ironic that the Christian Baldwin, who rejects the Black Muslim school, should sound so much like an adherent of X's segregation of the races:

The real reason that non-violence is considered to be a virtue in Negroes…is that white men do not want their lives, their self-image, or their property threatened.

This is bold, polemic language intended to get a rise out of whites and blacks.  I thinks it (and your quote too) is verbal fireworks only, not a call to arms for real ones.  It's an essentially Marxist argument: advocacy of the proletariate revolution.

Baldwin says that whites essentially like the quiet, passive, Uncle Tom, house Negroes because their non-violent existence allows whites to retain aspects of the master class: property, status, and self-image.