If it rains on election day, turnout drops about 50%. You think a ton of people are going to go wait in line at the DMV or wherever for a day to get a new ID they don't need for any reason other than to vote? Hardly... So, when they tweak the law to prevent people with a particular form of ID from voting, it doesn't really matter that in theory they could go get a new ID. In reality, the number of people from that group who turn out to vote will drop off dramatically. That's election fraud.
Let me give you a counter example. Driver's licenses from the state in which you live with your current address are something your typical Republican almost certainly has. Rural people have to drive everywhere, so they all have driver's licenses. Republicans are probably less likely to move around the country a lot, so they're very likely to have an ID from the state in which they live, and they're often more settled down in a house, so the address is more often up to date. So, requiring a driver's license from that state with your current address doesn't really create a barrier to Republicans voting. But, not everybody is living that lifestyle. People in big cities often don't get driver's licenses and they often move frequently both between states and within states because in cities you more often rent rather than buy and people in big cities often move around the country pursuing career opportunities that are more national than local.
So, lets reverse it. Say that we set up a voter ID law that requires that instead of a driver's license, you have to present a bus or subway pass to vote. The same arguments would apply. If the folks who don't have bus or subway passes want to vote, they could just go buy one. In fact, it's much easier than getting a photo ID. But, in practice, way more Democrats have bus and subway passes already. So, in reality, that law would mean that Democrats would win every election. At least enough Republicans would be too lazy to go get a bus pass that they couldn't win elections really in any state anymore. On top of that, the Republicans would have to divert huge amounts of their campaign spending to helping Republicans get out to get bus passes, as the Democrats are having to do now to get people out to get driver's licenses. It would be massive election fraud.
Well, this is the same thing in reverse.