There have been a lot of answers so far to this question, but most of them never refer to any evidence.
One very simple hypothesis is the following. By the time people get to be 18, their personalities are fully crystallized. The college system in the US then acts to filter these people into two different broad categories, based on the intellectual and behavioral characteristics they already possessed at age 18. College selects for kids who were already good at arguing and critical thinking, and willing to act according to the norms of the white-collar workplace (e.g., turning in paperwork on time). As evidence of this, there is a test called the Collegiate Learning Assessment, which is designed to measure critical thinking ability. Among college freshmen, about 32% of the variance in CLA scores is explained by their SAT scores, and by the time they graduate, this drops only a tiny bit, to 30% (Klein, p.18). Gains in critical thinking over the course of a college education, as measured by the CLA, are rather small: 0.18 standard deviations over the first two years of college (Arum, p. 35).
So in the population of the US, we have some people whose critical thinking skills are low enough that they would believe, for example, in the birther conspiracy theory, which Donald Trump was one of the earliest and most influential supporters of. These people are less likely to go to college and graduate.
Some answers have suggested that going to college exposes people to more diverse people, which makes them less racist and therefore less likely to be Trump supporters. This is a two-step hypothesis, and the evidence doesn't seem to provide much clear support for the first step. The first few papers I turned up in a google search on this kind of thing (Fischer, two papers by Wodtke) did not seem to clearly support it. It is true that controlling for racism and sexism reduces the effect of education on Trump voting so much that the 2016 election looks like previous elections (Schaffner), but since there doesn't seem to be much evidence that education cures racism, this three-way correlation among education, racism, and Trumpism is probably not one in which education plays a causal role.
There is also a clear correlation between education and rural/urban lifestyles. For example, 21% of people in Mississippi have a college degree, while in California it's 33%. The US two-party system is very strongly correlated right now with urban vs rural, and it's therefore natural that it correlates with education. So again, there are strong, obvious reasons for education to correlate with voting behavior not because education causes voting behavior but because preexisting characteristics cause both.
So in summary, a college education correlates with voting against Trump, and also correlates strongly with a number of personal traits, but the evidence does not seem to support the notion that college education causes any of these things.
We should also keep in mind that college does not make people into civil libertarians (60% of college students say the first amendment requires equal time for opposing views on a college campus), and that both liberals and conservatives in the US are susceptible to conspiracy theories and pseudoscience (think anti-vaxxers, or Alice Walker promoting David Icke).
Arum and Roksa, Academically Adrift
Schaffner, B., MacWilliams, N., & Nteta, T. (2018). Understanding white polarization in the 2016 vote for president: The sobering role of racism and sexism. Political Science Quarterly, 133(1), 9–34., https://onlinelibrary.wiley.com/doi/full/10.1002/polq.12737
Wodtke, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3883053/ , https://www.asanet.org/sites/default/files/attach/journals/dec18spqfeature.pdf