Filter all queries with a specific taxonomy

Below code is an example that does what you want. See tax_query for more information.

function my_get_posts( $query ) {
    // we only need to modify the query for logged in users
    if ( !is_user_logged_in() ) return $query;
    $current_user = wp_get_current_user();
    // assuming that user's region is stored as user_region meta key
    $user_region = get_user_meta( $current_user->ID, 'user_region', true );
    $query->set( 'tax_query', array(
        array(
            'taxonomy' => 'region',
            'field' =>  'slug',
            'terms' => $user_region
        )
    ));
    return $query;
}
add_filter( 'pre_get_posts', 'my_get_posts' );