It will be great when the NYT and other news outlets stop feeling the need to misrepresent the promoters of the standard trade agenda as "free traders" as they did in a news article discussing Donald Trump's latest actions on trade. In fact, these people are selective protectionists.
While they are happy to reduce barriers that might protect manufacturing workers from competition with low-paid workers in the developing world, they are fine with the protectionist barriers that maintain the high pay of doctors, dentists, and other highly paid professionals. (For example, a foreign doctor cannot practice in the United States unless they complete a U.S. residency program.)
They also support longer and stronger patent and copyright protections. These protections are equivalent to tariffs of thousands of percent on the protected items, most importantly prescription drugs.
The predicted and actual effect of this policy of selective protectionism is to redistribute income upward. Calling it "free trade" gives it a justification it does not deserve.