All 4 presidents on Mount Rushmore were protectionists.
Free trade is a theory that only works on paper, much like socialism.
I'd have to vehemently disagree with your comparison between free trade and socialism:
Personally, I think socialism is just as much of an epic fail on paper as it is in practice. It's just that it's proponents made a buttload of huge mistakes in their paper justifications!
In terms of Mount Rushmore, one of the Presidents was also a guy who thought all power should be centralized in the federal government.

Plus, a lot of work has been done in economics since the time of Washington and Jefferson, so their endorsement of protectionism doesn't necessarily mean it's the right course of action.
As far as free trade goes:
I certainly disagree with all of the managed trade legislation passed off as "free trade." On principle, I tend to feel that no government should restrict who you are allowed to buy from or sell to...
In practice, it's a tough call, but I'm still willing to give real free trade a chance. On one hand, prior experience has shown us that what we know as "free trade" has pretty much only resulted in our manufacturing base going overseas, due to the fact that much of the world is still developing and different countries are not even in the same ballpark in terms of wealth. On the other hand, prior experience has also told us that "capitalism" is the devil, yet we here at RPF know damn well that the system we're under is not actually free market capitalism. Also, even this not-so-free trade we have now has allowed us to buy crap we don't need for dirt cheap - and it's tough to determine how much more expensive things would be otherwise if we didn't benefit from the added efficiency trade and specialization offers. In any case, just like we haven't really seen the unhampered free market in action, we haven't really seen unhampered free trade in action, either. I'm personally willing to give it a fair chance, but only after we fix our own failed domestic economic policies, which would interfere and skew the results if left unchanged.
Besides, our manufacturing base would probably not have gone overseas anyway were it not for massive levels of taxation and regulation and our inflationary monetary policies. Manufacturing products offshore and selling them back to US customers is extremely inefficient for companies compared to manufacturing them in the market where they're sold, and the only reason dirt-cheap foreign wages compensate for the shipping costs and other costs is that taxes and regulations make it unreasonably expensive to manufacture in the US. Nevertheless, I've heard that even now, some industries have reversed their trend toward outsourcing, since it's
still not always worth it.