Anyone claiming to be a free trader, and for free markets, who does not also advocate absolutely open borders and free movement of labor, is just a half-assed free trader who thinks they’re advocating the cool theories the think the cool people should advocate.
And the free movement of labor, as it should, opens up entire other debates, where something other than the supposed lowest production cost of goods and services must be considered.
But anyone not also advocating the free movement of labor, or open borders, is a phony free trader and a phony free marketer.
Anyone who suggests that free traders must necessarily be in favor of open borders without understanding (or recognizing) the above is just a protectionist looking for a phony argument, and finding a particularly weak one.