If you were a poor person who really only has the value of their physical labor to feed your family you might not want to waste spend hours and hours of your incredibly (relatively) valuable time for something you can make do without. Since these poor people are often minorities voter ID laws disproportionately affect them.
The question of racism being a factor for supporters of voter ID is kinda muddied. Voter ID laws seem to make a ton of sense on the surface, but a little bit of knowledge about the American election system makes it clear that voter fraud is really not a big problem. There's no doubt that racists would support voter ID laws as they do suppress the election turnout of the poor, but I haven't seen any evidence that racial factors contribute to the majority of people's support for voter ID laws. Like every topic in US politics, it has become hyper-polarized to the point where both sides talk past each other to try to demonize their opponents.
[1]: https://www.quora.com/Why-is-DMV-so-slow
[2]: https://www.sacbee.com/news/politics-government/capitol-aler...