Hmmm. I can only speak as a layperson and not a tax adviser, but it sounds to me like you’re a Massachusetts resident, mainly because of the health insurance. I think if you filed taxes in another state, your insurer would drop you.
You might remember that in the debates over the Affordable Care Act (aka Obamacare), one of the cost-cutting plans suggested (but not successfully passed) by Republicans was allowing people to buy insurance from other states to increase market competition. Which tells you pretty clearly that buying insurance from companies in states where you don’t live is not currently allowed. Massachusetts insurance = Massachusetts resident.
If you want to establish residency in D.C. instead of Massachusetts, switch your health insurance ASAP, and then ideally start paying taxes in D.C. (if relevant) and switch your I.D. and voter registration over, so that it’s clear you’re really a resident there.
A higher-uncertainty “grey area” option is that if you know you aren’t going to move back to Massachusetts after your time abroad (or at least plan to establish residency in another state first), and you’re comfortable with dropping your insurance (which probably doesn’t cover you in Mexico) and maybe not voting, Massachusetts probably won’t come after you for taxes.
They way they handle this is they look at you after you move back to the state and see whether you owe back taxes plus penalties, and you go to court and argue over whether you were a continuous resident or not. Massachusetts doesn’t, like, have extradition with Mexico. Intent really does matter — a family friend who lived overseas for more then a decade before returning to Massachusetts never paid taxes and never had to, because it was clear he didn’t have an intent to return when he left — he hadn’t left any stuff there and was surprised to have moved back. The court agreed he’d behaved reasonably. Much like proving abandonment in a divorce proceeding, it’s your judgment whether you’re willing to bet you could win a case like that if you needed to.
Seriously, though, that health insurance is a clincher.
If you do want to pay your Massachusetts taxes from across the border, it’s slightly annoying right now, because they’re switching their website around, so the old website (which worked great) won’t exist after November 6, but the new one (which I’m automatically suspicious of without any reason to be) won’t be fully functional for individuals until December 5. Once that settles down, they promise it will be pretty easy again to do quarterly estimated withholding and to find free e-file places.