Hide a custom taxonomy's input box while leaving the other admin UI alone

gistfile1.txt

function remove_my_taxonomy_boxes()
{
	$tax_name = 'my_taxonomy';
	$content_type = 'post';
// presumably there is some condition you want to check, like current_user_can('something')
	$remove = true;  
	if ($remove)
	remove_meta_box( $tax_name.'div', $content_type, 'side' );
}

add_action( 'admin_menu', 'remove_my_taxonomy_boxes' );