That "liberals" now call themselves "progressives" is evidence of the corruption of the word "liberal." The use of "progressive" is an obvious semantic dodge, an effort to avoid association with what "liberal" has come to mean: a proponent of the nanny state.
As far as I can tell, all "liberals" (and "progressives") are Leftists: anti-libertarian statists extraordinaire.
P.S. A Cato-type libertarian probably thinks that such "rights" as abortion-on-demand and same-sex marriage are manifestations of liberality, in the old-fashioned meaning of the word (see Noun 1. here). In fact, abortion-on-demand and same-sex marriage are not manifestations of liberality, they are manifestations of statism because they are (or would be) state-imposed -- which is what "liberals" want.
If abortion-on-demand and same-sex marriage were manifestations of liberality, they would have arisen from voluntarily evolved social norms. That they have not done so means that they are destructive of the social order -- of civil society -- upon which liberty depends.
By the way, segregation in the South was state-imposed.
Some related posts:
Why I'm Not a Democrat or a Liberal
Left, Right, What's the Difference?
The Liberal Mindset
The Meaning of Liberty
Social Norms, State Action, and Liberty
For much more, click on Leftism - Statism - Democracy