Indeed, the Heritage Foundation's Economic Liberty Index suggests that, actually, there's little to no necessary contradiction between social liberalism and economic freedom.
For instance: Heritage hammers Denmark and Sweden for high levels of government spending but both countries are ranked "freer" than the US in matters as non-trivial as business, trade and investment freedoms. Indeed, Sweden and Denmark each score better than the United States in seven of the ten areas measured**. (Britain comes out 5-4 ahead of the US with the property rights fixture ending in a draw. Germany is tied 5-5 with the Americans. Canada, Australia and New Zealand also do better than America.)
This would probably surprise a lot of people in both the U.S. and Europe. The Heritage Foundation is a rock-ribbed conservative think tank, not some squishy-left house, so these results can't really be accused of left-wing bias. The U.S. does rank higher than some of those countries in overall economic freedom, because it wins bigger in some categories than it loses in others, but the point is that different countries prioritize different goals. In fact, different countries have different conceptions of what constitutes freedom in the first place, and this shows up in the rankings. This leads to the scenario we see now: a lot of countries ranked pretty close to each other in overall economic freedom, but with strikingly different formulas to get there.
There's a widely-held belief in the U.S. that Europe is a socialist wasteland, and a myth in Europe that America is a cowboy capitalist casino. But just because this belief is common does not mean it is not wrong. (I once shocked a European when I said that the U.S. financial sector was more heavily regulated before the crisis than the European financial sector; this person refused to believe me and in fact laughed in my face, but it's a true statement.) European economies are not at all monolithic, and cannot be lazily categorized in any one way. Different European societies choose different political and institutional arrangements that emphasize different outcomes, and some of these are to the right of America.
In terms of the marketplace of ideas, this is a very good thing. When different states follow different paths in organizing their domestic economies, it allows us to compare ideas to see which work better than others. It allows us to adopt positive aspects of other systems while avoiding others' mistakes. It gives us the ability to draws the lines where tradeoffs must be made, and decide intelligently how to make those choices. I think Patri Friedman's "seasteading" movement is pretty pie-in-the-sky, but political competition can be as good as any other type of competition, and there's certainly nothing wrong with learning from others' successes and failures.