I use a screen reader and visit Stack Overflow mostly. So, I can chime in for how things stand now (early 2022).
For consuming information, the site is minimalistic and quite a trial to navigate. The main issue seems to be the lack of HTML based on semantic structure. Since I fall into advanced screen reader users, I can overcome some of the usability issues, but it is still a serious time sink to develop these tactics. I would love to skip links and "copy" functions for code. Also, a way to navigate major contribution entries (like each answer). I personally have not used the up/down voting feature as context is too hard to determine if I got the correct controls.
As for contributing, I am finding some huge issues. I am new to this facet so I may be missing something, but this just highlights that things just aren't obvious. For me, it is the SE editor. In my experiences so far, it is unusable. I edit my text outside and cut and paste into the editor and pray.
I have turned on keyboard shortcuts in preferences as well as the alpha editor. And now I am editing.
Thus far, the shortcut keys for "navigation" of the page is not working, and I have found another person providing even further details on this. I believe there has been some improvements since the linked post, but the bulk remains true. See this post: Stack Exchange's keyboard shortcuts are not accessible to visually impaired users.
My attempt to use the editor to improve this answer illustrated the focus conflicts in impressive detail. When I had an unchanged buffer, I could use standard navigation (line and word movements) and even text selection. But as soon as a single change happened, the experience went wild and became unpredictable, and I fled to an outside editor to get this editing done. Perhaps someone can point me to a sandbox-like way to testing the contribution features without confusing the community with a "stunt" question/post?
In summary, the editor jumps out of editing mode if I use any cursor navigation. If I did manage to keep it from disengaging the screen reader, then it is super simple to "navigate" out of the editor section and jump out of editing mode again. So, you spend tons of time just trying to fix a typo due to all the state jumps happening from the screen reader trying to figure something out in the madness.