In Screen Reader Mode (v 3.0), it is not possible to edit a Confluence page which has been edited using the regular editor, therefore it is not possible to use and edit regular Confluence templates either.
To solve this problem, an administrator can create barrier-free templates, see Creating Barrier-Free Templates (v 3.0).
How to Use a Barrier-Free Template
In screen reader mode, all available barrier-free templates are shown above the title input field.
You can insert a template by clicking on the radio button and then "Apply template".
Image 1: Applying an accessibility Template (click to enlarge)
After applying a template, the template's text will appear in the text area below.