Post Object Filter by Custom Field, not title (ACF)

Question

There’s another filter for the post_object: acf/fields/post_object/result, that lets you customise the result (text) displayed for each option in the post object field.

Try something like this:

function my_post_object_result( $title, $post, $field, $post_id ) {

    /* Get whatever value you want here e.g. */
    $short_title= get_field('short_title', $post->ID);

    /* do any other processing you might want to do before returning it... */ 

    return $short_title;
}

add_filter('acf/fields/post_object/result/name=product', 'my_post_object_result', 10, 4);

Reference: ACF Documentation for acf/fields/post_object/result