Custom Post order for homepage

From a naming standpoint it seems that the term “filter” would be more appropriate since you are filtering by criteria first and then a sort (directional) is applied when you order. But that’s more a naming convention standpoint…

From a code structure if you are using the check_for_popular() method in several places then it makes sense to structure it as you did. If this is only for the filtering of the function I would go with a switch statement on the args for WP_Query and then execute the query. Something along these lines:

function mp_home_loop() {
    global $wp_query;
    $filter_args = array();
    switch( get_query_var('sort') ){
        case 'popular':
            $filter_args = array(
                'meta_key' => 'popularity_score',
                'orderby'  => 'meta_value_num',
                'order'    => 'DESC'
                );
        break;
        case 'trending':
            // obviously assign your own query args
            $filter_args = array(
                'meta_key' => 'trending_score',
                'orderby'  => 'meta_value_num',
                'order'    => 'DESC'
                );
        break;
    }
    $wp_query = new WP_Query( wp_parse_args( $filter_args, $wp_query->query_vars ) );
    include( CHILD_DIR . '/mp_home_loop.php' );
} 

Depending on how this query is being used (as in if it is driving your main query) then you might want to migrate this further into a pre_get_posts hook; however, since you mentioned that it was for the homepage I am assuming you have this a particular subsection of the page.