WP Query and order by particular specified IDs

To keep the same post order as it was passed to the post__in parameter, you need to pass post__in as value to orderby argument and ASC to the order argument

$query_args = [
    'posts_per_page' => $products, 
    'no_found_rows'  => true, 
    'post_type'      => 'product', 
    'post__in'       => [161,165,131,202],
    'orderby'        => 'post__in',
    'order'          => 'ASC'
];

EDIT

Looking at your edit, you have a bad filter somewhere, most probably a bad pre_get_posts action or a posts_orderby filter. Do the two following tests

• Add 'suppress_filters' => true, to your query arguments, if that helps, you have a bad filter

• Add remove_all_actions( 'pre_get_posts' ); before you do your query, if that helps, you have a bad pre_get_posts filter

• A third, but most probable useless check would be to add wp_reset_query() before the custom query, if that helps, you have a bad query somewhere, most probably one using query_posts