Every day all across this country people of all different races fight the police and don't get shot. Whether you get shot or not depends heavily on the cop and the situation.
This doesn't mean that there isn't a white privilege in the justice system. There is. Let's make no mistake about that. It exists and it has been proven. Among the different studies done it has been found that black people who commit crimes on average receive harsher sentences and an average of 20% more jail time than white people who are convicted of the same crime. At the same time if a black person commits a crime against a white person they are likely to get a harsher sentence than if they had committed the same crime against another black person or than a white person who had committed the same crime against a black person.
Here is a good piece that gathers together a bunch of different information taken from various studies that have been done over the years.
All this said, I believe whether or not you get shot by a cop actually has very little to do with the color of your skin. It has much more to do with the experience level of the cop, the confidence level of the cop and the situation surrounding the shooting.