You can listen to John Sides, a political scientist who has studied this topic here, starting at 15:30 and ending at 37:24.
It's well worth your time if you want to understand why some white working class voters voted for Obama in 2012 but moved to Trump in 2016. That's because Sides' research has something other studies of the 2016 elections lack: A data bank of the political opinions of the same 8000 individuals over several years.
This allowed him to see how a person's attitudes and opinions in, say, 2011 seem to have influenced that person's vote in 2012 and also in 2016.
That resolves several problems cross-sectional studies done on, say, the level of a county in 2016 have. For instance, if a county went for Obama in 2012 but for Trump in 2016 a cross-sectional county-level study cannot tell us why that happened. Perhaps those who voted for Obama in 2012 stayed at home in 2016 in greater numbers or perhaps those who voted for Trump in 2016 stayed at home in 2012 in great numbers or perhaps a large number of voters switched parties etc.
But Sides' longitudinal data is about individuals. This makes it possible to learn more about those white working class voters who voted for Obama in 2012 but for Trump in 2016. A short summary of his findings on that:
First, what didn’t matter: Sides finds that, despite Trump’s deviation from GOP orthodoxy on trade, there wasn’t a “statistically significant relationship between trade attitudes and vote choice in either election.” And while Trump voters had more negative perceptions of the economy, that had about the same impact on voters’ decisions as in 2012.Sides also notes that the most recent movement of many white voters without college degrees to the Republican Party is older than the last election, and could be observed from 2009 to 2015.* This suggests that those who shifted from supporting Obama in 2012 to supporting Trump in 2016 may already have been in the process of changing their political party affiliation.
“What stands out most, however, is the attitudes that became more strongly related to the vote in 2016: attitudes about immigration, feelings toward black people and feelings toward Muslims,” Sides writes in his essay. “This pattern fits the prevailing discourse of the two campaigns and the increased attention to issues involving ethnic, racial and religious minorities in 2016.”
Looking back at 2012, the path for Trump to convert some Obama voters on these issues was clear. Among whites who voted for Obama four years ago, about a third already held views on these cultural attitudes that align more with Trump’s rhetoric. Thirty-seven percent of white Obama voters had a negative view of Muslims and 33 percent said illegal immigrants were “mostly a drain” on society.
If Sides is correct in the above summary, the votes of the white working class Trump supporters might have been impossible for the Democratic Party to keep, even with a different presidential candidate.**
The interview doesn't mention measures of sexism and I haven't had time to unearth the actual study to see if this is because the 2011 attitude measures didn't include sexism or if attitudes toward gender equality did not change from the 2012 election to the 2016 election. Given that the 2016 election was the first one in which one of the two major candidates was a female I would have expected measures of sexism to correlate with shifting from Obama to Trump over time.***
----
* A reverse movement, Sides argues, is taking place among whites with college degrees. They are moving from the Republican to the Democratic Party.
** Sides states that his results show a correlation between feelings of economic anxiety and negative attitudes about immigration (and perhaps about Americans of African ancestry) which makes it difficult to attribute the changes to just one cause.
*** A cross-sectional study carried out right after the 2016 elections suggests strong levels of resentment toward working women among Republicans, especially among men but also among women, and considerable levels even among Independents and Democrats. Because that study is cross-sectional, it cannot tell whether those attitudes were equally strong in 2012 or whether a female Democratic candidate made them stronger. I'm planning to review that study later this week.