[TL/DNR: taking in only STEM majors wouldn't make a lot of sense, but it wouldn't be the end of the world either. If I were a betting man, I'd say they will end up with some completely arbitrary ratio that we will make up a rationale for after the fact.]
A lot of people in this thread are misunderstanding the Navy's perspective in regards to leadership potential and the ability to become tactically proficient. It is absolutely true that your college major is completely unrelated to those two traits. If you sift through 1000 STEM majors and 1000 baristas you will get two near-enough identical results as to make no difference. I haven't seen anybody make a valid argument to the contrary, and I don't think the Navy has some secret study showing otherwise either. What the Navy is really doing is saying that since it can get the same leadership and tactical abilities regardless of which major pool it draws from, why not get them from a pool of STEM majors that may (possibly, in a few limited situations) add other benefits later?
Granted, I don't agree with that outlook because I don't think that the need for those STEM majors is that great. Yes, Nukes, AEDOs, EDOs, and TPS represent needs (self-defined, in some of those cases), and filling slots at NPS represents a desire, but outside of the acquisition and maintenance worlds - and there only to a limited extent given the extensive civilian support - I don't see how all this "technical" capability will ever be used.
But just like the need for STEM majors is overblown, I'd also say the fear that we are somehow losing something irreplaceable by having fewer non-STEM types around is pretty much groundless. The claim that the non-STEMs have some sort of magical way with words is stupid for multiple reasons, not least of which is how large a percentage of Navy writing is just FITREPs/EVALs and ppt briefs (and seriously, those two forms of communication are at best one step advanced from throwing feces at each other). I'm also not concerned about a lack of poli-sci and history majors in our ranks causing an increase in difficulties interacting with other countries/cultures. By the time anybody is senior enough to interact with another country in a meaningful way, the Navy has long since become the dominant driver in their outlook and knowledge base.