Custom Post Type Not Visible to Other Administrators in WordPress

Check the Screen Options tab in the upper-right corner of the Menu administration screen. Does a checkbox for the post type appear and need to be checked for that user?

If that’s the case, the default checked/unchecked boxes are likely controlled by the default_hidden_metaboxes filter when $screen->parent_file is nav-menus.php.

Also see https://wordpress.stackexchange.com/questions/20505/make-item-checked-by-default-for-all-users-in-screen-options-pane, which uses that filter for Dashboard meta boxes, but the same functionality is used for showing/hiding menu options.

Top, this is the trick!