One thing I want to say in support:
The argument in favour of free trade is that it increases the pie, so that everyone can be better off (a Pareto improvement). However, given that trade does produce winners and losers, this argument is predicated on redistribution, namely (over)compensating the losers.
That second part of the argument in favour of free trade is often conveniently forgotten. So when that redistribution doesn’t happen, then opposing free trade is quite rational for some.