Drupal - Hide or disable field after registration

If you want to do it in custom module

my_module_form_user_profile_form_alter(&$form, &$form_state) {
  // Since it is on registration form, field might be reqruied.
  $form['your_field']['#required'] = FALSE;
  $form['your_field']['#access'] = FALSE;
}

You can try Field Permissions Module

Features

• Enable field permissions on any entity, not just nodes.
• Role-based field permissions allowing different viewing patterned based on what access the user has.
• Author-level permissions allow viewing and editing of fields based on who the entity owner is.
• Permissions for each field are not enabled by default. Instead, administrators can enable these permissions explicitly for the fields where this feature is needed.