SOM vs Sloan

I'd echo what bb said. I can say for sure you'll find like-minded people at Yale SOM. And you should absolutely look into the loan forgiveness program given where you want to be post-MBA. If you are eligible for it, it'll take the burden of student debt off your shoulders, which makes a huge difference.

Congrats on getting into great programs!
I would say MIT Sloan hands down for this one! First of, MIT Sloan's Mission statement is “To develop principled, innovative leaders who improve the world and to generate ideas that advance management practice.” These aren't just words in the air. Sloanies live and breathe these words! Etched in every wall, every classroom, every project, every study trek!
Companies such as The Bridgespan Group (Bain), Dalberg, New Sector Alliance (Accenture), Education First, B Lab, ClickHealth, Department of Energy, Endeavor, Education Pioneers, Helion Venture Partners, Stonyfield Farm, Millennium Promise, Samasource, United Nations, Women’s World Banking recruit at Sloan all the time.
Sloan has the "Sustainability Certificate" and there are soo many students taking the courses for it, gearing towards careers in Non-Profit Consulting, Social Entrepreneurship, Non-Profit Management, Multilaterals and CSR.

I'd advise you to lookup the "MIT Sloan Sustainability Initiative" to look at all the resources, classes, treks, groups, etc. Sloan pours many resources into this field, and have amazing faculty. Every year they give out the MIT Sloan Social Impact Fellowship (SSIF) to EVERY student who does an internship in the field. The Fellowship funds students interning over the summer at local, national, and international social impact organizations.
And if you want traditional management consulting, Sloan will open those doors no problem. Want law school classes? Sloan lets you cross-register with Harvard Law School (or any Harvard graduate level class <HBS, HKS,etc>, or broader MIT class) since the curriculum is so flexible after a first semester core. Don't turn down Sloan, its reputation alone will open any door you need.
Best of luck!

On a per capita basis, I do think SOM has MIT beat in terms of MBB offers. Additionally, they're huge on social impact, so you may find that combination attractive. I think you'll truly be able to find more of your "people" at Yale, but I understand that MIT is hard to turn down. It does have a Sustainability Certificate that you can do, but I feel its social impact is more tech-driven (see Legatum Fellows). If you want to go into developmental consulting, I think Yale is just a better fit for it.

I am a Yale SOM admit as well and have had the opportunity to meet with a number of alumni, current students and other fellow admits.
Your analysis with respect to SOM seems to be spot-on. SOM definitely seeks to build socially conscious leaders and you will find a number of like-minded peers.
The ratio of people getting into Management Consulting is very much on par/better than many other M7 schools and the CDO & Consulting Club seemed to be top-notch.
You will have great diversity within the class as well as the opportunity to take classes across Yale.
Other factors worth noting are that the faculty:student ratio is much lower than peer schools and in the words of the acting Dean, Yale has an environment where the faculty genuinely care about and interact closely with the students. The percentage of the school budget that comes from student tuition is among the lowest (if not the lowest) meaning that you will get more bang for your buck.
Sloan is undoubtedly a great school but given your career preference, SOM seems like the right choice.