The left is concerned about voter suppression, but the simple requirement that a voter present a valid ID at the time of voting isn’t what most people, including most Democrats, perceive to be suppression:
The survey doesn’t provide further cross-tabulated data, but it looks like white Democrats are close to split on the question. All other major subgroups, including non-white Democrats, are on board with the requirement. Hispanics, the putative victims of voter ID requirements, support it by a margin of nearly 3-to-1.
You wouldn’t know it listening to the pundit class talk about the issue. Requiring an ID is no more a poll tax than writing a check for groceries or picking up a pack of cigarettes is. Making a big fuss about the requirement is a good way to sow distrust in the process.
In contrast to the elites, regular leftists put a lot of moral emphasis on perceived fairness. This is an illustration of as much. Voter ID requirements do marginally benefit Republicans but a majority of Democrats still support them. Civics isn't quite dead yet.