Has America changed since the 1960s? Yes. Selma and Birmingham no longer happen. Is racism gone? Ohhhhhh, no. And racism, bigotry and, well, raw political power get manifested in different ways nowadays. This is why the result of the U.S. Supreme Court's overturning of parts of the Voting Right Act is likely to be reduced opportunities for blacks, Latinos -- really, anyone who's not white and conservative -- to vote. That means we won't see a return of the dark tactics of poll taxes and literacy tests -- again, American has changed in the last half-century. That does mean we'll see the continued proliferation of voter ID bills in Republican-dominated statehouses, especially ones in states where minorities -- Democratic party-friendly minorities -- could be inhibited enough from voting to keep the GOP in office.
To a degree, this is about pure political power, even removing any racial element. The strongest supporters of the Republican Party are whites. White are a shrinking percentage of the population. The strongest supporters of the GOP don't like policies favored by non-whites...non-whites who are likely to vote Democratic. Remember, there's always someone in a primary who can out-conservative you. So, do the logic: if your voters won't let you change your policies lest you lose a primary, and there's a smaller and smaller ratio of those voters in the big picture, you try new means of building back the ratio. Like keeping the other, growing group from increasing its ratio. The way to do that is to make voting as difficult as possible.
The racism comes in the sentiments of some (not all, obviously!) of the GOP base, like the ones who still oppose immigration reform when the latest bill is projected to reduce the deficit -- supposedly a top concern of the Republican base. As long as this latent racism and bigotry survives, GOP politicans (some of whom surely share those sentiments) will legislate to reflect this worldview, and will pass laws to keep from voting the ever-increasing number of those who oppose that worldview. (The good news is that Section 2 of the Voting Rights Act still survives and can stop similar voter ID efforts like the one in Wisconsin.) America has changed, but not enough.