We have the same debate with early voting, how long polling places are open, and where they are located.
For whatever reason, conservative voters tend to be more motivated to vote. So any friction in the voting process tends to disproportionately affect Democrats.
As an aside, there are structurally racist policies that suppress Democratic votes both historically and today. To give one example, most states do not allow exconvicts to vote.
As to why many Americans are opposed? Because for so long this country has tried to prevent anyone but white men from voting.
Besides that, voter ID is a solution in search of a problem. There’s just not a plausible way to commit large scale fraud at the polls. You’d have to round up bus loads of people willing to commit voter fraud, take them from polling place to place, then have them sign their names as some other voter on the rolls at that polling location and hope that the real voter hasn’t and won’t show up to vote. I lack the imagination to see how this could occur without detection.
In any case, what everyone should actually be concerned with is that the voting system accurately captures the will of the people. In which case, voter fraud at the polls, in America, is the least of our problems. Our attention should be focused on things gerrymandering, first past the post, and for presidential elections, the electoral college, among other issues.