ACF Post Object meta-query by title not ID

It can be done, but it won’t be so easy. Post Object is stored as an ID, so you can’t use meta query to search by post title in such case… There are few ways of solving that problem:

1. Use acf/save_post action to save title of given post object as another meta value:

// Add this to your functions.php
function save_intervention_country_name ( $post_id ) {
    $country_id = get_field( 'intervention_country', $post_id );
    if ( $country_id ) {
        update_post_meta( $post_id, 'intervention_country_name', get_post_field( 'post_title', $country_id ) );
    }
}
add_action( 'acf/save_post', 'save_intervention_country_name', 20 );

And then you can search using intervention_country_name field:

$wp_query->query(  array (
    'post_type' => 'intervention',
    'meta_query' => array(
        array(
            'key' => 'intervention_country_name',
            'value' => <COUNTRY NAME>,
            'compare' => '=='
        )
     )
));

2. Use posts_where and posts_join filters to modify SQL query.

You’ll have to add a JOIN statement to join your post object field with posts table, and then add where searching by title.

3. Modify your form in such way, that it does the search by ID not by name.

So if there is a select field, then fill its values with IDs. Or if you can’t do that, you always can get the country first and then use its ID:

$country = get_page_by_title( <COUNTRY_NAME>, OBJECT, <COUNTRY_POST_TYPE> );
if ( $country ) {
    $wp_query->query(  array (
        'post_type' => 'intervention',
        'meta_query' => array(
            array(
                'key' => 'intervention_country',
                'value' => $country->ID,
                'compare' => '=='
            )
         )
    ));
}