The way I think about it is that trade enables people everywhere to focus their energy on their comparative advantages. That reduces the potential benefit of moving to another economy that benefits a more different set of skills.

One way to think about it is that westerners are going to lose those jobs either way (and to more or less the same people), because it is more efficient for the low-skill low-wage workers to do them. The difference between free trade and protectionism is whether the low-skill workers move to the western economies or stay where they are.