True or false?
A competent economist must answer true. A move to free trade redistributes income among producers and consumers. If those who gain do not compensate those who lose, economists have no basis for concluding that the move to free trade is a good one. On the other hand, this does not imply that free trade should not be adopted either. What the economist can do is help society focus the argument in the proper framework so as to keep the losers from getting away with nonsense arguments to the effect that free trade will reduce efficiency, destroy the economy, and so forth. The losers' only valid reason for opposing free trade is that they lose from its adoption.
One reason why nonsense arguments are so prevalent in debates about the merits of free trade is that arguments based explicitly on self-interest are not persuasive. A more effective approach is to try to persuade the listener that his/her own interests are served by the position put forward---an even more effective approach is to scare the listener into believing that catastrophe will result from free trade (or restricted trade, if one is arguing for the other side).
Economists also can point out that all technological improvements have gainers and losers, as does every policy the government can adopt (including a policy of doing nothing and letting economic developments take their course). Indeed, it is widespread recognition of this fact that makes arguments explicitly based on self-interest unpersuasive. If efficiency is pursued at every turn, most people will sometimes gain and sometimes lose, but on average will typically gain. Everyone is worse-off as a result of losing their own special benefits from particular inefficiencies, but will gain even more on average from eliminating the inefficiencies that benefit other people. People who end up losing overall then have a better case for claiming compensation on grounds that circumstances have done them badly.
This having been said, however, it still pays any individual to adopt whatever arguments will persuade society to shift rents in his or her direction.