Many of those who fought for voting rights prior to the First World War were indeed Republicans. This was, of course, in the days when the Democrats were dominated by the Southern arm that was focused on maintaining Jim Crow. Woodrow Wilson was perhaps the most racist president of the 20th century - and given some of the other luminaries filling that role before 2000 (*cough* Reagan *cough*), that's saying something.
The real irony is that the current Republican Party wants to move back to these days not to rejoin the fight for social justice, but to bring back the reasons it had to be fought in the first place. They've adopted the mantle not of the progressive-minded Republicans of the prewar era, but of their Dixiecrat opponents.
I'm reminded of the scene in Clockwork Orange, where Alex, upon reading the Bible as a sign of personal improvement, is shown imagining himself not as Jesus Christ, but as one of the Roman guards whipping him.
Added on edit to clarify - I am not, in any way, defending the NC-GOV candidate, nor am I defending the modern Republican Party in any way. I'm just pointing out that the broader scope of history allows modern charlatans to make rhetorical points, especially if historical facts are stripped of their context.