I ended up using a simple meta_query
:
$args = [
'post_status' => 'publish',
'post_type' => $post_type,
'orderby' => 'title',
'order' => 'ASC',
'meta_query' => array(
'relation' => 'OR',
array(
'key' => 'my_acf_field',
'value' => $search_term,
'compare' => 'LIKE'
),
)
];
$query = new WP_Query($args);