Compared to almost 4 years ago, when this first post was written, much has changed.
WordPress has now an active accessibility team with the full support of the lead and release developers.
The last 2 months we worked on accessibility standards for WordPress core, to be added soon to the overall code standards in the codex. Everything that gets into WordPress core, has to comply with the Web Content Accessibility Guidelines (WCAG) 2.0 Level AA standard.
Therefor we are also writing a Handbook to help developers, give examples on how to code and how to test with accessibility in mind.
Our main goal is that WordPress core conforms to WCAG 2.0 Level AA. This includes the Admin section and all bundled themes (like Twenty Sixteen).
Andrea Fercia is working hard on the issues still present in core, with the help of other developers and committers. For this we set a roadmap with issues to fix for each major release.
To test WordPress we can ask the help of our test team of a11y experts and users of assistive technology.
So far about WordPress core.
On WordPress.org thousands of free themes are available, written by volunteers. These theme developers can add the accessibility-ready tag to their theme. This ensures that some basic accessibility is taken into account. The number of accessibility-ready themes is growing every week.
The requirements for this tag are basic (heading structure, keyboard accessible etc.), but that way the biggest issues are tackled.
Speaking for myself: I’m very positive about the future of accessibility of WordPress core.
The big task now is: get the developers and designers educated. Most want to code or design accessible, but have no idea how. That is why we still need to keep reviewing and testing new code that gets into core.