Why are libertarian so often right-wingers?

I was reading EconLog a couple of days back and it brought back to the surface a question I have been asking myself for a while. Why are libertarians so often associated with the right wing? Specifically, why the Republican Party in the USA. Let us look at the Republicans and the Democrats and evaluate them according to libertarian values:

Economic Issues

Republicans advocate for a "small government" which trusts the market to do what it does best. Goods and services are best priced by a free undistorted market. Republicans also advocate fewer taxes (which is a big bonus when it comes to respecting private property) and an unregulated labor market without price controls or contracting restrictions. That is the conventional wisdom.
However, we should not forget things such as the Republican stance on immigration. Republicans are much more likely than Democrats to oppose open borders. Why? Keep American jobs for Americans. In other words: Knee-jerk protectionism. Libertarians realize that the job market is not a pie that you have to divide between foreigners and locals. Instead, an influx of cheap labor drops prices boosts consumption and helps everyone. (Somebody may have lost their job, but overall, we are better off) Also, who loves those rural voters and throws them farm subsidies as often as possible? Also, it is a historical fact that Republicans are much worst at balancing the budget than Democrats. And eventually, that bill is going to come due...

I would give Economic issues to Republicans by a slight margin.

Foreign Policy

Democrats it's well known are all peace loving hippies. That's a far fetched exaggeration, but recently, the Republicans started two wars where neither accomplished a whole lot. Whether it is Afghanistan or Iraq, it is hard to argue with the fact that the Democrats were a whole lot more committed to peace than the Republicans were. Now, it would be unfair to forget things such as the Balkans war which Clinton jumped in, but comparing the recent records of Republicans and Democrats, the Democrats seem less likely than the Republicans to get involved in wars.

I would give the Foreign Policy issues to the Democrats by a slight margin

Social Issues

This is in my opinion where the big difference is. Whether you are talking about abortion rights, gay rights, minority rights, women's rights, etc, the Democrats can carry this one home easily. The Republicans are a whole lot more likely than the Democrats to tell you what you can or cannot do in your bedroom. And that for me is a deal breaker. If we also look at things such as religious freedom and discrimination, it seems the Republicans would be a whole lot more amenable to racial or religious profiling.

Social issues in my opinion go easily to the Democrats.

So, why is it that Libertarians associate so much with the Republicans? Are the economic issues so immensely important that the slight Republican advantage in that area overshadows everything else? I had that chat with a friend of mine recently who said: "Well, I'm in favor of abortion rights and letting whoever want to marry do so, but I'm a white heterosexual guy. It's not my issue. Economic policy on the other hand affects me a lot." I think some of it may be that point. We are closer ideologically to the Democrats, but the dimensions on which we are more "left-wing" are not those most closely aligned with our self-interest. So we are likely to go with the other side. We'll grumble and kick and scream, but in the end, we'll get seduced by a little bit more of free-market. Now the question is: Should we keep on doing that? Or should we switch to the other side?