Peter cannot publish pages in Community Edition. MGNLUI-2939 added a new availability constraint writePermissionRequired=true to activate and activateRecursive actions. This has the side effect that Peter, whose demo-project-publisher role doesn't permit him to write to the website workspace, cannot publish pages either.

This issue is specific to CE since it doesn't have workflow.

(In EE, Peter can approve a workitem. The new action availability constraint was not added to /modules/workflow/messageViews/publish/actions/approve.)

Update:
This was introduced with: MAGNOLIA-5795

In 4.5 we had workflow as part of CE and peter was never able to 'activate' anything on a workspace. He was only able to publish from workItems from the inbox.
As we changed this in 5.0 by removing workflow from CE, peter should now be able to publish in CE (which conflicts with his readOnly permission on the workspace).

One possible solution is to change the writePermissionRequired to 'false' in CE and switching it to 'true' when installing workflow for that app. which IMO is only an ugly workaround to a conceptual problem we're facing.

OTOH, why should peter be able to push something to a public instance (which is a much more harmful action) and not be able to publish (activate) something which is more likely do much less harm, than pushing it to public. My vote goes for reverting or at least change the default of the writePermssionRequired to 'false'.