Charles Zelden wrote The Battle for the Black Ballot, one of those short form accounts of landmark Supreme Court cases, this one concerning Smith v. Allwright. This case served as the true death sentence to the "white primary," even if it was in some fashion run by the party itself. Note that the Twenty-Fourth Amendment, dealing with poll taxes in federal elections, specifically includes "primary" and other elections in its text. This underlines that simplistic interpretative rules are problematic -- in various cases, this might be seen as implying that amendments without "primary" are less all inclusive. Note as well that the Supreme Court used the Fourteenth Amendment to attack state poll taxes.
The all white primary was but one disenfranchisement technique, a myriad of "neutral" laws (including still lingering examples such as felon disenfranchisement aka former felon disenfranchisment, since we are not just talking about people in prison or even on parole/probation) put in place toward this end. Such laws also sometimes targeted other "wrong" sorts, such as poll taxes that in some cases were clearly in place also to harm poor whites. An understanding of history would help in seeing behind the neutrality, including in cases involving "at large" voting that historically was used to dilute the voting strength of local black communities. Missing the forest for the trees, such things look perfectly fine.
See also, various Republican voter suppression techniques. John Stossel has an idiots shouldn't vote piece up. I'm not sure many of his (conservative) supporters would want to know how that would work in practice. BTW, I recently saw the second half of Recount, the HBO movie about the 2000 mess. I'm reading a book by Zelden on the matter as well. Depressing, but useful. Unlike some, I cannot "get over" the hijacking of a presidential election. Blacks did not "get over" early defeats in white primary cases.
Disenfranchisement and dirty pool tended to stick in their craw.