No, they like the socialized medicine. Specifically, they like to claim that a lower infant mortality rate means Cuban health care is better than in America. It doesn't take long to see through that. America does not abort at the first sign of trouble, like Cuba does, and so America has more babies that don't live very long.
Abortion is not the issue in this case, except to show that abortion rates are not a bellweather of health care. What is a bellweather of health care is the health of the country overall. Cuba's cholera epidemic shows that its health care system, which they present with pride, is not all that terrific.
Cholera is controlled by really simple sanitation standards. That is the most important aspect of health care, not pictures taken in hospitals. Like claiming technology superiority if elites have a computer but no one else can, showing off hospitals while people die because feces is in the water is not a model America should emulate.
Instead, as small steps toward privatization have taken hold, Cuba is instead trying to be more like America.
Poor Countries Are Unhealthy Countries By Roger Bate, Real Clear Markets