If you argue Chakotay is racist you should also be making the same claim for Bashir.
...He's Arabic, right? Did they, perhaps, think the character would not be likable if he had an Arabic accent or showed any signs of having an Islamic background?
Of course that's not what they were thinking. That's just how they wrote the character, and he happened to be given an Arabic name because the actor is from an Arabic background. Chakotay's spiritualism stuff is more an effect of lazy research.
But if Earth is one unified government, then the human population should be about 1/4 Asian and 1/4 Arabic, no?