I disagree somewhat with both you and the person you're responding to. I don't think it's explicitly the engineering or math that is upsetting them, and I don't think it's "brainwashing". The real problem is that, when you get a broad education and actually learn about the world we live in, modern Republican ideology is revealed to be complete insanity.
I think that misses the underlying causes.
Both Leftism and Conservatism are fundamentally about identity, which is social. People don't care about economics they way they do social issues, economics only determines how much money you have, but social policies determine which tribe is winning.
Conservatism is fundamentally about creating a peaceful safe community, that's why they tend to be more supportive of law enforcement, more outwardly patriotic, and less tolerant of diversity, they want a strong unified community. The idea of Conservatism is people should be be free to do whatever they want, and the way to ensure that is a strong community that ensures that people only want things that are good for the community.
Leftism champions individual liberty so that you're free to truly express yourself, that means that law enforcement should only be used as a last resort, group identities are viewed with suspicion, and people should only be part of the communities they want.
Universities are about learning and research, and those work best when people are free to experiment and push intellectual boundaries, ie leftism. That's why Universities will always have a tendency to lean left.