I am able to recreate this issue. It only happens on pages where the permissions are set to only allow Authenticated users through the normal page permission flow. To me this indicates that the Feather templated pages aren't built to honor the page permissions set within the system.
I created a new MVC-only template and successfully published an Auth'd-only page without error, so it's limited to the pages that utilize Feather.
I am able to work around the problem by doing the following:
1. Create the Bootstrap templated page.
2. Add controls and publish.
3. View and receive error.
4. Break inheritance and set to Everyone.
5. View and no error.
6. Change back to inherit from parent (Auth'd only).
7. View and no error (with proper auth redirection working when tested).
Seems like a bug to me.