Since I'm not a trade expert, I suggest you check our web site and the issue briefs which can be downloaded. There should be quite a few.
We don't have group positions. On trade I suspect assorted staff economists come to it in their own way. I prefer to let others where I work speak for themselves.
My three favorite reasons for rejecting free trade doctrine are:
a. Social consequences follow from transactions across borders, no less than those within them. If it is acceptable to regulate the latter, there is no reason not to consider regulations on the former. Free trade is nothing but the international version of free markets, which often don't produce results (e.g., "externalities") we find acceptable.
b. Trade policy or lack thereof affect a nation's industrial composition, and by extension its income distribution. Measures aimed at promoting equality often -- but not always -- have economic costs. So "industrial policy" via trade rules is a legitimate concern. There remains, Brad, the matter of effectivensss of any such policy, in terms of the intended beneficiaries and potentially neglected third parties.
c. Free trade in financial assets is a manifest disaster. Only idiots fail to see that now. Unfortunately they are still running our Fed and Dept of Treasury.
mbs