However, so what? The motivation is irrelevant. It's well-established that minorities are less likely to have photo IDs, and are more likely to face significant hurdles obtaining them, so a law that makes possessing a photo ID a requirement for voting is a racist law. That the racism was probably motivated by political considerations instead of hatred (and that the laws are also classist, ageist, and often sexist) doesn't make it less racist, nor less odious.
Also, I'm not willing to completely rule out racial animus as a motivating factor for the politicians voting for those laws. The Republican Party is not an intrinsically racist organization, but it is extremely tolerant of racists and has invested a lot of time and effort into trying to recruit them into the party. That was the whole point of Richard Nixon's Southern Strategy, after all: to bring conservative white Southerners, many of whom had moved away from the Democratic Party because of its support for the civil rights movement, into the Republican fold. The GOP didn't abandon appealing to while racial resentments as a campaign tactic after Nixon was elected in 1968, and one has to assume that at least some of those new recruits ended up being elected to office.
But again, so what? Voting for a racist law is a bad thing to do regardless of your motivation.