In a recession, demand for business output declines. Businesses respond to lower revenue by seeking to cut expenses. With wages exhibiting downward rigidity, businesses cut their wage bills by firing workers, which swells the ranks of the unemployed.
The Keynesian response would include transfer payments to the unemployed, but it would also include stimulus spending, which goes to firms and then to the workers who have retained their jobs. This increase in wages during a recession is on top of the real wage increase they already received by keeping their jobs at their old pay rates.
Unless we're saying that the share of stimulus spending that businesses pass on to labor is used ENTIRELY for new hires, and that unemployment benefits fully offset lost spending power of the recently unemployed, the Keynesian response to a recession exacerbates economic inequality.
I'm sure I'm not the first person to think this, but I wonder why many of those who most-loudly advocate a Keynesian response to a recession are the same lot that most-loudly bemoans economic inequality, and they never see fit to justify the one view with the other.