How to get selected taxonomy or category ID if using custom walker?

May be easier to just work with it, than against it…

Instead of:

$cat_id = sanitize_text_field($_POST['cat']);

Try:

$cat_name = sanitize_text_field( $_POST['cat'] );
$cat = get_term_by( 'name', $cat_name, 'category' );
$cat_id = $cat->term_id;