I don't want to be depressing, here, but - how do you cope with it?

[LeftyMom]

33. Identify a problem that's within your reach, do something about it.

Lather, rinse, repeat.

Burnout is usually caused by struggling with problems that are too big for you to handle, in my experience. Or trying to solve everything in one go. Successful social movements never, ever work that way.

Practice self-care. If you feel yourself getting overwhelmed it's okay to choose to step back or shift gears. If the bank account is running low you don't donate your grocery money, so if your energy and enthusiasm are running low don't take on a project you don't have it in you to do well right now. Say no sometimes, an activist community where one person does all the work isn't healthy. Don't be that person and if somebody else is step up and lighten their load (and be aware that if their identity is in being a martyr to a movement that they're likely to resist assistance.)

So back to your OP, the problems that you list are overwhelming and some of them are probably lost causes. Some of them are problems that exist because of people you don't know in places you may never see, where your leverage is non-existent. You can't fix all of them, no one person can. But you have it within you to work diligently to create change in some small part of one of them. You find that part and you do your best, and you know that other people are doing the same with their little parts of bigger problems, and that that's how movements work. And you educate other people and grow the movement. Especially that.