You need not be a fan of Donald Trump to say that trade has had a big impact on manufacturing jobs, you really just need to be someone in the reality-based community. Unfortunately, a lot of people who should, and probably do, know better are insisting that trade is not a big deal. The story is that we lost the jobs due to productivity growth, not trade.
There are three points worth making here. The first is a simple logical one, we have a trade deficit of around $500 billion a year, a bit less than 3.0 percent of GDP. This is basically all due to a deficit in manufactured goods (we have a surplus on services). Does anyone believe that the extra imports associated with the trade deficit are not associated with jobs? Can $500 billion worth of manufactured goods be produced without hiring people? (This matters much more in a context where we face secular stagnation, meaning there is not enough overall demand in the economy.)
The second point is that our trade deficit has not always been this large. Our deficits had been around 1.0 percent of GDP through most of the period from the late 1970s until the East Asian crisis in 1997. Following the crisis, the value of the dollar soared and the trade deficit did also. It eventually peaked at almost 6.0 percent of GDP in 2005–2006. (I should be giving the non-oil deficit, but I'm too lazy to look that up just now.)
Anyhow, this explosion in the trade deficit coincided with a sharp decline in manufacturing employment.