The Mapbox web interface uses the open-source Leaflet.js library plug-in ( http://leafletjs.com ) to display web maps, so Mapbox adherence to accessibility standards is directly dependent on Leaflet meeting these standards.
Leaflet is currently not section 508, but they are working on it. There is currently a big discussion on Leaflet GitHub on this topic: https://github.com/Leaflet/Leaflet/issues/3210
The biggest problems are apparently related to the base plates (screen readers will read the file name of each tile) and the map control buttons.
(Note that this answer is definitely relevant to their Javascript library. I'm not sure about my iOS or Android SDK.)
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