Skip them.
MRE are not a subsistence food. Being in the military you should be familiar with the various colorful translations of the acronym ("Meals Ready to Expel" is my favorite.) They're a stop-gap until proper mess facilities can be put into place.
They're also hella expensive. If you can get them for free, cool. Otherwise MRE are a waste if you're homeless.
You'd be much better off getting something like an emergency ration bar. They're not meal replacements but they keep you from hurting too much when you miss meals. They also have enough fiber that you won't end up not crapping for a month. Taste-wise they're "meh" quality shortbread but they help quite a bit.
They're also packaged as one unit so if you open one bar, you're eating that whole thing within a few days otherwise they go stale pretty quick.
Supplement that with veggie-heavy Subway wraps (don't do sandwiches, the bread fucks you up) and stay hydrated. Stay away from sodas or juices. If it's hot, a Gatorade will help replenish electrolytes but you don't want an even bigger sugar spike.
Dried fruits and meats will be good but they're pricey.
Resist the urge to go for fast food on the regular. Every once and a while it's good to get a nice big Mickey D but do not make it a habit or you'll end up gaining weight and generally feeling like shit.
Get a decent can opener as well. Canned food isn't the most appetizing food on the planet but in a pinch you can do quite a bit with a few bucks at the dollar store.
Every few days get a cup or so of plain Greek yogurt to help keep your stomach in check.
Don't sweat about coyotes. They're generally harmless and will scatter if you so much as cut a loud fart. Just be smart about your food, don't leave it unpacked. Tie it into a bag and hoist it into a tree if at all possible. If you're really that concerned, get a table leg or an axe handle or something to use as a whackin' stick.
Get some small condiment containers as well. Salt is a necessary mineral plus it makes "meh" food more tolerable but other condiments can make that thing you've eaten five times in two days more edible.
If you're able, get an insulated water bottle/container. It's one of the things I really wish I'd had when I was homeless because you can have cold water with you all day and when it's 100+ it feels like a goddamn miracle.
Best of luck to you.
Why not MRE's?