I moved away from for profit orgs to work for a social movement org a few years back.
Your best bet is to find orgs that you like, and reach out to them. Some may have a careers page, others won't. Mostly you can expect to get contracting gigs if you form a relationship with them. These places rarely have a tech team and usually outsource anything technical.
If you're accustomed to working in tech circles with well defined roles and working with people who know what it takes to build software, be warned that you won't find that at most other places outside of tech, especially if you're thinking about orgs that deal with addiction or mental health. Be prepared to explain concepts you took for granted (like sprints) to a lot of people.
