Historically, voting restrictions in the US have meant the minimizing of political agency amongst minority groups. In particular, following the era of Reconstruction, the rise of Jim Crow laws in the former Confederacy saw the implementation of measures designed to remove the right to vote, in violation of the 13th/14th amendments. The Civil Rights movement of the 1960s culminated in the Civil Rights Act, which, as we know, the US Supreme Court recently gutted. The laws we see passing now—requiring official photo ID to vote, among others—privilege individuals who conform to a certain socioeconomic status, while removing groups like African-Americans and Hispanic immigrants from the political process. These groups typically vote Democrat. That many of these anti-voter measures are put in place by Republican lawmakers certainly creates doubts about the intentions of the laws.
Stricter voting laws tend to impact Democratic voters at a disproportionate level. While Democrats do come from all walks of life and economic classes, the majority of disadvantaged and underprivileged voters do vote Democrat. Stricter voting laws impact many more potential Democratic voters than Republican voters, and I don't think anyone who's remotely researched this issue can argue with that.
Research suggests that stricter voting rules affect democrats more since it suppresses Democratic votes more than Republican ones. Out of sixteen states eight have voted so far and new voting laws have been implemented in these states. Evidence suggests that Democratic voter turnout dropped by 37% and was 285 percent worse in states enacting new voting laws.
Based on the previous elections and the history, stricter voting rule affected the Democrats more than Republicans. As the data indicates, Democrats are hit hard from the stricter voting ID rules as it impacted the minorities who generally vote for Democratic party. Hillary or Sanders may need to appeal to all the public to vote for them in big number despite of the ID rules.