Will everyone in the world eventually become the same, mixed race?
Agree
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Yes, most likely. There will be some holdouts in the isolated tribes of the Amazon or the multitude of Andamanese islands though.
Disagree
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It depends on what "eventually" and "mixed" means. If "eventually" means in a thousand years then evolution will do its thing and people will more and more intermingle, but it will take a long time. If "mixed" means 50-50 then this will also take a long time, if ever. But if "mixed" means, say <1%, of another race, then this has happened already for most people in the US already!