Throughout most of its history, the Democratic Party was a logically improbable coalition of southern whites and northern workers, most of them were either immigrants or the direct offspring of immigrants. The two disparate groups were brought together by a common adversary: northern Protestant businessmen and farmers. As a result, there were always elements of both class and identity within the party, but the identity part predominated.
As the party slowly came to embrace the aspirations of African-Americans, who were denied any meaningful role in politics between Reconstruction and the 1960’s, the southern whites moved away and became Republicans for cultural, not economic, reasons. The party has consequently remained a coalition of victims, but one united in opposition to the rule of white Christian men, not just businessmen and farmers. The swing voters today are middle-class white women and white working men, both of whom have either economic or identity ties to both parties.
The bottom line is that the Democratic Party has always had both class and identity components. It cannot afford to renounce either if it wants to be successful on a national level.