They're relative socialists (compared to neoclassical libertarians) in the sense that they think government intervention is needed to compensate for the deficiencies of capitalism. The most extreme intervention would be government ownership of the means of production, as in Obama's taking over of the banks in 2008. But there are less extreme interventions such as antitrust law, raising taxes on the wealthy, government spending on social programs, and so on.
Are you asserting that Keynesian economists wouldn't tend to be socially liberal and to vote Democrat, while neoclassicals wouldn't tend to be socially conservative and to vote Republican? You're declaring there's no such political dichotomy among American economists, is that right?
On the syntheses of the two approaches:
https://en.wikipedia.org/wiki/Neoclassical_economics#Evolution
