I'm familiar with the Brennan Center. It's a left-wing advocacy group funded by George Soros. Slate is also on the Left, so these sources represent one side of the debate so what is needed is to compare and contrast how right-wing advocacy groups respond to the charges.

Here's another take I'm just throwing out there as a possibility. Let's say this is all partisan politics. Democrats want to do X with voting and Republicans want to do Y. Since the demographics for Democrats includes more blacks and Hispanics it is only natural that anything that adversely affects the Democratic Party as a whole will also affect them. Since Republicans have far more white voters than blacks and Hispanics, anything that Democrats push against Republicans would have a greater general impact on white voters. So if the demographics were equal, or closer to it, then there would be no claim of racial bias. With Donald Trump as the GOP nominee the demographics are even more one-sided, so it's easier to make the claim. But let's say Ben Carson campaigned better and won the nomination, and along with that African Americans and Hispanics started going over to the GOP. Then the demographics of the Republican Party would change and the claim of race as a factor might no longer be valid. Like I said, just throwing it out as a possibility. Not saying it's true or not since I haven't read the other side except for that one National Review piece.