the first is in failing to understand the class nature of the oppression, such that it is treated as "black people versus white people" when in reality it is "working class versus billionaire ruling class"
It's white people versus black people in the context of the civil rights movement.
The second error is in thinking there even is a non violent path in the first place, as the root of the problem is Capitalism, it has no conscious or empathy, and will sooner kill us all then give up it's power over us.
But most of the people that make up capitalism do. And nonviolent direct action isn't dependent on its opponent having a conscience or capable of empathy. The fact that so much of today revolves around money and making the most of it is beneficial to the nonviolent path because that creates avenues to resist through where or how we spend our money, or flat out ceasing to participate in xyz market altogether. Like Gandhi did with salt or King did with the smaller businesses of the cities they would target. It's far from perfect but far more effective than people (like you, your loved ones, or even your children or children's children) dying in droves just to accomplish something that potentially could've been accomplished without the loss of a single soul. The more fortunate and therefore the blind don't see this as a big deal because their lack of knowledge of the misfortune of losing someone close to them or of the experience of being in the thick of it themselves because of hate and violence, and the naive convincing their contemporaries that hate and violence is the only legitimate path.
Ultimately, regardless of what metaphysical beliefs one may have, nobodies "God" is going to come down and save us, we must save ourselves, and for that we must have solidarity, work together
King would completely agree with you; he rejected the bodily supernatural resurrection of Jesus, the supernatural and miracles within the Bible, and even the dogma of Pauline Christianity, though he still quotes and considers him plenty. King believed in God in the same way people like Socrates, Plato, Aristotle, and Albert Einstein did. That it's something completely beyond a humans comprehension and ability. Ironically, "scripture" and Jesus when he references this verse in Matt 5:33 when he warns of the woes of taking oaths, would also agree:
"Thus said Jehovah: The heavens [are] My throne, And the earth My footstool, Where [is] this — the house that ye build for Me? And where [is] this — the place — My rest?" - Isaiah 66:1