When people say they are upset about trade, I think that what really bothers them is that automation is allowing us to produce 85% more manufactured goods with far fewer workers. That transition has been painful for many workers, but it's not about trade---except in one respect.But factor-augmenting technical change augments different factors of production differently, and the political economy gets interesting.
Trade allows the US to concentrate in industries where we have a comparative advantage (aircraft, chemicals, agricultural products, high tech goods, movies, pharmaceuticals, coal, etc.) We then import cars, toys, sneakers, TVs, clothing, furniture and lots of other goods. It's likely that our productivity is higher in the industries where we export as compared to the industries where we import. So in that sense, trade may be speeding up the pace by which automation costs jobs. But probably only slightly; in previous posts I've shown that even within a given industry, such as steel, the job loss is overwhelmingly about automation, not trade.
Why do so may people blame trade? Cognitive illusions. It seems like imports would reduce aggregate demand, and that this would reduce employment. Those effects are highly visible. It's human nature to demonize foreigners. But even Paul Krugman rejects that argument, at least when we are not at the zero bound.
When farm work was wiped out by automation, uneducated farmers generally found factory jobs in the city. Now factory workers are being asked to transition to service sector jobs that have been traditionally seen as "women's work". Even worse, the culture is pushing back against a lot of traditionally masculine character traits (especially on campuses). The alt-right is overtly anti-feminist, and Trump ran a consciously macho themed campaign. This all may seem to be about trade, but it's actually about automation and low-skilled men who feel emasculated.It's more complicated than that: the industrial technology as the United States became more productive in agriculture was one that lent itself to Fordist division of labor, and nearly anyone could do the work. The techniques involved in designing and building the advanced technology goods of today seem less favorable to such an outcome, although perhaps the presence of reserve armies of people willing to work for less will induce that innovation. The culture wars are likely of second-order importance, if that.