The short answer: You simply can't argue with such a person. If you can't agree on a basic set of premises, then no meaningful argumentation is possible.
Consider the following discussion:
A: "The theory of evolution is supported by the fossil record, carbon dating and geological considerations" - B: "Satan planted all that evidence to lead the faithful astray and hide the real truth that the world was created in 6 days by God, sometime around 6000 BC." A & B will never agree on anything. This is a radical example of the fact that everything is theory laden.
The only way to convince such a person would be to prove that another part of their argument is based on the same data. For example, they might site government statistics that minorities are at a disadvantage in the job market or in college admissions compared to whites, at which point you could challenge them on why are government statistics acceptable in some parts of the discussion but not in other parts. You could force them to be consistent in there source of facts. But if they don't have any such inconsistencies, then it is indeed impossible to convince them otherwise.
A note on the #BlackLivesMatter topic: The issue is not whether more whites are killing blacks or more blacks are killing whites in general. Poverty, lack of education, and unemployment are higher among black people, and so it is expected that they would have higher violent crime rates than white people. This happens with just about any minority in a developed country.
The issue is whether law enforcement treats whites and blacks in the same way or not. From this point of view, government statistics clearly show that both law enforcement and the legal system are clearly biased in favor of white people.
Black get worse sentences for the same crimes. Police tend to react violently to black suspects while giving white suspects the benefit of the doubt. Blacks are more likely to get stopped and questioned by police officers, etc....
There is clearly a double standard in this country, and right now #BLackLivesMatter is the only movement addressing the issue. Eric Gardner was strangled and killed for selling loose cigarettes (regular tobacco, not even drugs), while Dylan Roof, who had just murdered 9 people in cold blood, was bought a hamburger by the cops who arrested him. Think about that before you debate #BlackLivesMatter activists the next time.