Because you're implying its because of their race. Not because of their economical or social advantages or disadvantages. Which one is racist?
One more time...
If there is a statistical correlation between Characteristic A and Characteristic B, anything that affects those with Characteristic A will, by extension, affect those with Characteristic B to the extent of that correlation. This is true even if there is no causal relationship between the two characteristics.
So, if I want to reduce the number of black or Hispanic people that vote, I would first look at the characteristics of those populations and notice that they are more likely to be poor than white people. So if I institute a policy that makes it harder for poor people to vote, I am affecting more black/Hispanic people than white people.
This accomplishes my goal. Sure some white people are affected, but that's acceptable because significantly more black people are affected. As a bonus, because I don't
directly target the minorities, I can argue that I'm not targeting race.
It's similar to how chemotherapy works. Chemotherapy is essentially giving the patient poison. That poison, however, is more lethal to hypoxic cells. It doesn't target cancer, it targets cells with low oxygen levels. Tumors tend to be hypoxic as you have an overgrown mass of cells with inadequate blood supply to deliver oxygen. So the doctors give the patient a poison that is more likely to affect cancer cells, though it will also affect some healthy cells, which is why chemo makes people sick. The hope is to kill the cancer before killing the patient.
Voter registration laws can do the same thing. Just substitute minorities for cancer cells, white people for healthy cells and poverty for hypoxic.
(Note: I'm remembering from my Radiation Biology class 28 years ago, so details may not be perfect. Might be conflating hypoxic with something else, but the point stands.)
I'm not against voter ID laws as long as they are accompanied by an effort to provide the required IDs to everyone who wants one with minimal effort.