Republicans prior to the 20th century were progressive and Democrats were conservative. The positions eventually reversed culminating with Reagan. Now the conservative Southerners who hadn't voted for a Republican since the Civil War vote almost exclusively Republican.
Regarding the tariffs, the tariff increase in 1930 had nothing to do with being progressive. Raising tariffs was a response to the depression when the government couldn't pay it's bills. Tariffs were raised to fight the deficits. Also, though Clinton signed NAFTA, I wouldn't exactly call him progressive.
IMO, the progressive position in any policy is the position which favors the disadvantaged or the advantaged. Although some people might argue lower tariffs help the poor by decreasing the cost of goods, I don't buy it. The poorest people in the country aren't buying that many manufactured goods to begin with since they don't have the money, and they are even less likely to have money if American jobs are destroyed by cheap imports. The people who benefit from cheap tariffs are the importers and the upper class, and the middle class Americans who still have jobs.
And as for immigration, I would also argue being anti-immigration is progressive. Historically, employers have used immigration to force down wages and laborers opposed it for the same reason. While it is progressive to want to help people from other countries improve their lives, it isn't progressive if you have to hurt Americans to do so.