Disable publish and unpublish options in VBO on the main content view for one role
Views Bulk Operations (VBO) contains a sub module called ACTIONS PERMISSIONS:


  A module called actions_permissions is included in the package. This
  module generates a permission for each action, and VBO honors those
  permissions before showing or executing the corresponding actions.
  This is useful if you want to provide your VBO to several groups of
  users with different privileges: the same view will accommodate those
  different groups, showing to each the actions that they are permitted
  to see.