I'm not disagreeing with your general point -- from my observations at a tech-focused school, many STEM folks write off the arts pretty hard -- but I think your examples are poorly chosen. Most folks are aware or have at least heard that, at a deep level, music has a lot of mathematics. Additionally, linguistics emerged specifically as a scientific study of language: much closer to STEM than other humanities.

A better example might be that philosophy/law require broad and deep contextual knowledge of prior thinkers and extremely strong logical skills. Even having trained in formal logic as a software developer, I sometimes struggle to parse philosophical arguments, even when laid out plainly. Yet, even that is still a comparison on the same plane as STEM when ultimately these fields come with different sorts of complexities. Apples and oranges.