The Dems could then tell Black voters "see, the Republicans are all a bunch of racists". That was even though Goldwater was not a racist and opposed the bill on principle (years later he regretted his opposition to the bill). And that was even though most southern Dem senators opposed the bill. Goldwater was crushed by LBJ in the '64 election, and Republicans received a far lower percentage of Black voters than in 1960.
The Republican Party has never recovered from that disastrous loss of a sizable percentage of Blacks. The Dem Party has convinced Black voters that only the paternalistic policies of the Dems can help them. Even though most of those policies have been unmitigated disasters for Black people. It will be a long uphill struggle to regain the same percentage of Black Republicans as the party had in 1960.
MLK was a Republican...