Any way around letters of recommendation requirement? I'd like to apply for an MBA (sick of working in IT and want to change) but seemingly every university I look at requires multiple letters of reference, one of which from a current supervisor.

Is there any way to get around this requirement?

I have zero trust in my current boss, and given that writing the letter would take effort for no benefit to him (since I'd be leaving the company and he'd have to find a replacement), odds are a letter by him would work against me. Also, I'd really rather not owe him a favor.

Former bosses/colleagues would be a safer bet, but I left my previous workplace about two years ago and haven't had any communication with them since (moving continents doesn't help either, I can't just invite them for coffee).

As an aside, how come one can't get access to higher education (not just MBAs) on their merits alone anymore? When I applied for my undergrad degree acceptance didn't depend on who one was friends with.
Your "merits" consist of more than just your undergraduate grades. They also consist of your ability to work with others, your curiosity, your interest beyond just learning what's necessary for the test, etc. This is why we ask for letters of recommendation.

As for who exactly writes your letters, there is more leeway. I don't know about MBA programs, but in mathematics we would usually be equally happy to get letters that do not necessarily include your current supervisor. I would imagine that letters from former supervisors would be just as acceptable. The point, however, is that your supervisors can speak to your work ethic and abilities in ways nobody else can, and consequently provide important insight to the committee evaluating your application that cannot be obtained in any other way. In particular, co-workers likely have a different perspective on you than what a former supervisor sees in you.