An example: In Texas, a student ID is not good enough to count as a voter ID -- but an NRA member card is. I kid you not. The Simpsons could not have come up with something more absurd.
Minorities in the US are way less likely to carry photo ID. I could go on and on. In short, the situation is different than in Slovenia.
Also, there's a loaded history, too. Blacks were disenfranchised post-Civil War through a whole host of measures, of which IDs was just one of them. Requiring IDs or literacy for voters brings back thoughts of Jim Crow laws. These issues are steeped in history that Slovenia just doesn't have.
Minorities in the US are way less likely to carry photo ID. I could go on and on. In short, the situation is different than in Slovenia.