Ordering posts by anniversary using only day and month

No, it’s not possible by using pre_get_posts alone. But you don’t have to use separate fields for the date.

WP_Query, although doesn’t provide a simple query arg that would sort the posts by month and day only, you can use the posts_orderby filter hook to modify the ORDER BY clause (i.e. ORDER BY <the part here>) for sorting the posts.

Working Example

1. In the pre_get_posts hook, set the meta_key to crimedate:

   // In crimes_orderby_meta():
   
   elseif ( 'crimeanniversary' == $orderby ) {
       $query->set( 'meta_key', 'crimedate' );
   }
   

2. Then on the posts_orderby hook, you can use the STR_TO_DATE() function in MySQL to sort the posts by the month and day of the meta value:

   Note that I purposely used a static leap year, which means 29/02 (Feb 29^th) always comes after 28/02 (Feb 28^th), when the sort order is ASC.

   add_filter( 'posts_orderby', 'posts_orderby_crimeanniversary', 10, 2 );
   function posts_orderby_crimeanniversary( $orderby, $query ) {
       if ( is_admin() && 'crimeanniversary' === $query->get( 'orderby' ) ) {
           global $wpdb;
   
           $order = ( 'ASC' === strtoupper( $query->get( 'order' ) ) ) ? 'ASC': 'DESC';
   
           // This means, we still sort by the date, but we "recreate" the date using
           // the year 2020 (or any leap year), and month and day from the meta value.
           $orderby = "STR_TO_DATE( CONCAT( '2020-',
               MONTH( {$wpdb->postmeta}.meta_value ), '-',
               DAY( {$wpdb->postmeta}.meta_value
           ) ), '%Y-%m-%d' ) $order";
       }
   
       return $orderby;
   }
   

I hope that helps, and please correct these issues in your code:

• In crimes_add_custom_column_make_sortable():

  $columns['crimeanniversary'] = 'crimeanniversary';  // like this
  $columns['crimeanniversary'] = 'Crime anniversary'; // not this
  

• In crimes_show_columns():

  get_post_meta($post_id, "crimedate", true)  // like this
  get_post_meta($post_id, "crimedate", false) // not this
  

  And just remove that line with $row_output — which is not defined.

• And don’t forget the fourth parameter here:

  add_action('manage_posts_custom_column', 'crimes_show_columns', 10, 2); // like this
  add_action('manage_posts_custom_column', 'crimes_show_columns');        // not this!