IF a school grantsboth BA and BS STEM degrees, then the former are perhaps worth of disdain, at the very least they wouldn't be designed to get you into a PhD program.
In another direction, I don't believe MIT has any BA degrees, and a quick check showed that if you major in music, you get a Bachelor of Science degree (abbreviated S.B. at least in the '80s). Of course, you don't graduate from MIT in any field without doing a lot of physics and the calculus, plus some other science requirements....
It's pretty arbitrary and dependent on the school. MIT thinks of itself primarily as a science school, so they only award BSes. In contrast, Oxford gives out BAs in everything, even math/physics/computer science.
In another direction, I don't believe MIT has any BA degrees, and a quick check showed that if you major in music, you get a Bachelor of Science degree (abbreviated S.B. at least in the '80s). Of course, you don't graduate from MIT in any field without doing a lot of physics and the calculus, plus some other science requirements....