I think the issue is that there are "economically liberal" politics (= free market above everything else) and "socially liberal" politics (e.g. pro gay marriage

I think the issue is that there are "economically liberal" politics (= free market above everything else) and "socially liberal" politics (e.g. pro gay marriage etc.). In the US, these are split between the Republicans (more economically liberal) and Democrats (more socially liberal). The party which is radically liberal in both senses is the (very small) Libertarian Party.