Mississippi also elected Republican Prentiss Walker to Congress. Had they put up Republican candidates in all 5 districts, they may have won them all.
That is complete and baseless speculation. There is zero evidence that White Southerners felt an urgent need to throw their Democratic politicians out of office (politicians that voted against the CRA, while most Republicans in Congress voted for it, so even with a Goldwater nomination, that whole theory just never held up) after 1964. The Civil Rights Act opened up politics in the South, there's no question about that; however, it didn't even kind of usher in an era of Republican dominance. Not even close.
The 1964 gains in the Deep South would have been greater than they were if (A) Republicans had contested every Southern district and (B) provided funding for such candidates.
In 1964, the GOP elected a Congressman in MS. Two (2) of its incumbent Democratic Reps, John Bell Williams and William Colmer, openly endorsed Goldwater.
Alabama elected three (3) Republican Congressmen (out of
, and they, too, would have swept the other Democrats out of office had they put up candidates and funded them. Georgia elected its first Republican Congressman since Reconstruction in 1964 (Bo Callaway). In SC, not just Strom Thurmond, but Rep. Albert Watson endorsed Goldwater and switched parties (although Watson's party switch didn't come until after the new Congress was sat. In LA, David Treen won 49% against Hale Boggs.
The GOP didn't really try to field candidates in many Southern states because the GOP was not a functional party. There were many Southerners who voted Republican for President by 1964, but almost all of them voted in the Democratic Primary for state and local offices, and their Democratic Congressmen had seniority which made them powerful. But the results in MS and AL showed that in the Deep South, voters were angry enough with the national Democratic Party that they would have thrown out the baby with the bath water.
I very much believe that if the 1964 election were close, and where the GOP didn't get blown out outside the South, there may have been enough momentum for House Republicans and Southern Conservatives to join together to form a new majority. Perhaps the Southerners would have been folded into the GOP; the time was right for it. It didn't happen because of the HUGE majority of seats the Democrats won nationwide.