This should work
function exclude_posts( $query ) {
if ( $query->is_home() ) {
$query->set( 'tag__not_in', array( 13 ) );
}
}
add_action( 'pre_get_posts', 'exclude_posts' );
tag and tag_id are not set up like cat to accept negative numbers (ID numbers) for exclusion (conclusion based on experiments, not digging into the code (some other time, perhaps!)). Also, all of the examples in the Codex use is_home(), is_admin(), etc., but apparently is_home does work – without the ().
