I was a double english and math (cs-emphasis) major. I went to grad school in Industrial Engineering/Operations research because I wanted to study a field where engineering type thinking is applied outside the traditional engineering fields.
The things I've learned in engineering and science classes constantly influence my thinking outside these fields. For example, I recently did a computer science programming assignment (coursera data structures) about percolation and phase transitions. Immediately, I started seeing the model in so many things - vaccine coverage in a population where people start to opt out, availability of housing, the dating scene as people start to pair off and get married. Any probabilistic process where things seem steady state until the last moment, and then a sudden shift occurs. I know my example may be a little trivial, but that's the point - some of these are silly, and probably very misapplied, but other times, they lead to extraordinary insight. My thinking about a very wide range of things is deeply influenced by may background in math and engineering. I constantly build math models in my head when I read the news. I see it as a basic form of literacy - and you only get it if you really engage with the kind of difficult math typical of STEM fields.
I really think that humanities students are in greater danger of ending up narrowly focused than science students. Even if I hadn't majored in literature, I (like most STEM students) would have had to take a substantial amount of history, art, literature, foreign languages, and so forth as part of my GE requirements in college. The math and science requirements are typically far less rigorous for humanities majors.
It's a terrible mistake to think that math, science and engineering aren't essential components of a broad, liberal education.