This is a freedom-based problem. First, what problem is voter id supposed to solve? Well, people cheating by voting illegally. Is this an actual, demonstrable problem? No. Despite grandiose claims by FOX News and Donald Trump, there is no evidence of widespread voting fraud. So we've established that this is a solution to a problem that does not actually exist.
Second, does it impact our freedom? Voting is both our right and responsibility as citizens. Should we be required to carry and show id just to prove that we are citizens? "Do you have your papers, citizen?" used to be a joke we made about the shortcomings of totalitarian communist dictatorships. So yes, it does impact our freedom, as we should be free to go about our day without carrying government id at all times, and I believe that would include the act of voting.
Limiting our freedom to solve fake problems sounds un-American to me.