Stop contributors from editing standard posts but allow them to edit a custom post type

Question

Hint

The changes on roles and no layout-topics should not a part of a Theme, is much more a topic for a plugin. maybe you think about this topic on point like maintenance, switch of theme and hooks for activation – easier on plugins.

For your problem

You must add the roles new capabilities for your custom post type and remove the capabilities for type post. On activation change the roles for the follow capabilities.

foreach ( self::$todo_roles as $role ) {            
     $wp_roles->add_cap( $role, 'edit_' . self::$post_type_1 );
     $wp_roles->add_cap( $role, 'read_' . self::$post_type_1 ); 
     $wp_roles->add_cap( $role, 'delete_' . self::$post_type_1 );
     $wp_roles->add_cap( $role, 'edit_' . self::$post_type_1 . 's' );
     $wp_roles->add_cap( $role, 'edit_others_' . self::$post_type_1 . 's' );    
     $wp_roles->add_cap( $role, 'publish_' . self::$post_type_1 . 's' );
     $wp_roles->add_cap( $role, 'read_private_' . self::$post_type_1 . 's' );   
     $wp_roles->add_cap( $role, 'delete_' . self::$post_type_1 . 's' ); 
     $wp_roles->add_cap( $role, 'delete_private_' . self::$post_type_1 . 's' ); 
     $wp_roles->add_cap( $role, 'delete_published_' . self::$post_type_1 . 's' );
     $wp_roles->add_cap( $role, 'delete_others_' . self::$post_type_1 . 's' );  
     $wp_roles->add_cap( $role, 'edit_private_' . self::$post_type_1 . 's' );
     $wp_roles->add_cap( $role, 'edit_published_' . self::$post_type_1 . 's' ); 
}

With something like the above you can add capabilities the roles.

You should also do this to remove all rights for the type post.

$wp_roles->remove_cap( ... )

As hint to the source. The self::$post_type_1 is a variable in a class for the custom post type. The foreach loop is to add this capabilities often to different roles.