Sacrilegious means extremely disrespectful towards something considered sacred. An action that causes deep offense to a believer — like burning a religious text, for example — is sacrilegious.
The Latin sacrilegus, "thief of sacred things," was used to describe robbers who plundered graves and temples. Anything that's sacrilegious is essentially as disrespectful as a graverobber towards things that others find holy or solemn and serious. In modern ironic usage, a sacrilegious opinion runs contrary to popular wisdom or deeply held beliefs. Calling the movie Citizen Kane boring and self-indulgent is totally sacrilegious to many movie lovers.