This Study (Cited by the Left) ACTUALLY Says Voter ID Laws Don't Restrict Voting

Approximately one in seven non-voters signaled a lack of possession of a state approved photo ID as one of the reasons they did not participate in the 2016 election. Among this subset of non-voters whose nonparticipation was attributed at least in part to the photo ID requirements, approximately two-thirds of those with a preference would have voted for the Democratic candidates.

However, when pressed to give the principal reason why they did not cast a ballot in 2016, only 1% of non-voters identified a lack of a state-approved photo ID as the principal reason they did not vote. Among this handful of non-voters, 86% actually possessed an approved form of photo ID, while 14% did not. While the photo ID law at least partially discouraged some people from voting, an actual lack of a state approved photo ID kept virtually no one (only one nonvoter among the 819 surveyed) from turning out to vote in 2016.

University of Houston study
https://uh.edu/hobby/voterid2016/voterid2016.pdf