How accessible are CMS default themes?

This varies widely, and you should not rely on the claim that a theme is accessible across the board. Even well-meaning themes frequently show basic defects in practice: missing landmark structures, insufficient color contrast, mega menus that cannot be operated by keyboard, poorly marked-up sliders or missing focus indicators.

On top of that, conformance always depends on the overall picture: even a solid base theme can acquire barriers through your own customizations, page-builder elements or embedded modules. The delivered state of your live site is decisive, not the theme's demo state.

An audit shows precisely which adjustments your specific theme needs, and whether these can be implemented in a targeted way or a switch is more sensible. More on this under accessible web development.