In Noah's Curse: The Biblical Justification of American Slavery, Stephen R. Haynes writes:
By the mid-1960s, the legal status of segregation had been settled in America's courts and political chambers. But segregation's staunchest proponents continued to fight, insisting that integration was the leading edge of a social revolution bent on "overthrowing God's established order."
As conservative Christians reacted to what they regarded as perilous change, they pressed Nimrod's legend into service. One example is Corey Daniel of Dallas, a Baptist preacher who utilized the legend to depict integration as part of a demonic social scheme. ...Daniel combined race and disorder in his portrait of Nimrod, "the Negro leader of the Babelbuilders (Gen 10:6-10), whose name means 'Rebel.'" [...]
Like many Southern conservatives, Daniel associated the campaign for civil rights with socialism, internationalism, and revolutionary dictatorship. In fact, the alliance between integration and the loss of individual freedom is exceedingly close in Daniel's mind. Using epithets such as "those first unholy one worlders" and "the United Nations' modern tower of Babel," Daniel applies Genesis 11 to popular anxieties about America's role in a changing world. [...]
Like the Babel-builders, the UN seeks to integrate races and governments, "lest [they] be scattered abroad upon the face of the whole earth." Again like the architects of that ancient UN, the modern internationalists "are ignoring, when they are not actively blaspheming, the Lord Jesus Christ and His glorious gospel blood redemption." Thus, in Daniel's view, Nimrod is the patriarch of all schemes to consolidate in rebellion against God.
Let's keep in mind that we are talking about efforts to desegregate America's schools and other public institutions. This should have been viewed as a question of basic justice: black Americans were denied justice, equality, and freedom on the basis of nothing more than racial bigotry by whites. Many of these whites sought to defend and justify their racism, their bigotry, and their institutional discrimination on the basis of their religious texts.
Few if any were just cynically manipulating the Bible in the service of racist political goals. We should accept them as completely sincere in their beliefs, which probably only makes things worse. The fact that blacks were being denied justice and equality was, in their minds, less important than the fact that giving them justice and equality would have undermined long-established social structures. They believed that the subjugation of blacks by whites was designed by God as the desirable social order in America — that God was in effect a racist just like them.
Notice also that Daniel, like others, equated racial desegregation with a loss of freedom. This is no different from the arguments made by conservative evangelicals today that equal rights for gays will lead to a loss of freedom. These people view liberty as a limited commodity: giving others basic freedoms that one takes for granted for oneself must necessarily lead to a decrease in freedom for others. Of course, any loss of freedom for white Christians is a sign that Satan is working behind the scenes.