Historically this is easy to understand. The Confederacy was primarily a vehicle for the interests of rich white slaveholders. It was also directly at odds with the interests of the Southern poor, whose wages were perpetually undercut by the persistence of free labor, and whose lives were disproportionately sacrificed in its defense. To win their support, the rich worked to cultivate a culture of racism rooted in last-place avoidance and investment in the status quo; but this appeal had limited traction outside of the middle class, for obvious reasons.
Direct memory of this class conflict certainly survives among the Southern poor, who were raised to remember the Civil War as "the rich man's battle and the poor man's fight"; but its legacy also persists in the politics of Neoconfederacy, which remain grounded in opposition to the federal government as an agent of redistribution. Even if they happen to harbor racist attitudes, the poor still have little stake in opposing federal economic intervention, and significant reason to support it.
Perversely, the Liberal stereotype of "poor white trash" can itself only be understood as a form of classism - it is ignorance of the plight of the southern poor rooted firmly in privilege. Liberals, sheltered in the relatively prosperous urban north, had little need to acquaint themselves with the history and views of the southern poor. And as David Williams writes, it seems "to gratify the pride of many northerners to think their ancestors defeated a united South," a kind of "regional vanity" that leads them to "generally demonize white southerners." Today, as capitalism immiserates North and South alike, vilification of poor southerners functions as yet another expression of last-place avoidance.
What Liberals and Neoconfederates both have in common: enduring bigotry cultivated in the service of class.