Drupal Home page permission
This question was asked on the Drupal forums here. 

If your frontpage is a node you can control access using the Content Access module.

If your frontpage is being generated by a custom module then you can do it by modifying the hook_menu implementation in your module. You can change the access_callback to the value TRUE so that everyone can access that page. See this related question


  "access callback": A function returning TRUE if the user has access
  rights to this menu item, and FALSE if not. It can also be a boolean
  constant instead of a function, and you can also use numeric values
  (will be cast to boolean). Defaults to user_access() unless a value is
  inherited from the parent menu item; only MENU_DEFAULT_LOCAL_TASK
  items can inherit access callbacks. To use the user_access() default
  callback, you must specify the permission to check as 'access
  arguments' (see below).


See the full documentation here.