Look at the data from the data source used in that stack exchange.
https://www.washingtonpost.com/graphics/national/police-shoo...
white killed by police: 495 (49.5%)
black killed by police: 259 (26.1%)
hispanic killed by police: 172 (17.3%)
other: 67
About 13% of the US population is black, and 12.5% is hispanic. Both groups ARE over-represented in police shootings, with black people being about 2x more likely to be killed than their population figure would suggest. Compared to the way this is portrayed in the news, however, I would suggest that these figures already run contrary to the narrative that this is primarily dictated on the basis of racist behavior by police. The fact that there are more white people killed by police annually ALONE (despite their larger representation in the population) is a fact that most people would be surprised to hear.
What really offsets the data is once you begin to include racial statistics on crime. Obviously police officers aren't just taking individuals out of the population and random and killing them (isolated outliers not included), so it would be irresponsible to just compare the racial component of police shootings with population representation. This data, however, varies greatly by area. However, in urban environments in particular, the racial component in crime is enormous. In Chicago, for example 75.3% of homicide was committed by black people, 24.6% by hispanics, and 3.5% by white people. To expect equal representation in police shootings, given those crime statistics, would be completely insane.
So the long story short is: given a straight comparison to population distributions, there is an overrepresentation of black/hispanic shootings by police. With the inclusion of racial participation in violent crime though, the motivation for police fatalities cannot responsibly be attributed to a racial motivation without a serious multivariate analysis.