General Synonyms:
* Disrespectful
* Impertinent
* Insolent
* Impious
* Sacrilegious (if referring to religion)
* Profaning (if referring to something sacred)
* Blasphemous (if referring to religion)
* Unreverential
* Flippant
* Mocking
* Satirical
More Specific Synonyms:
* Iconoclastic (challenging established beliefs or institutions)
* Subversive (seeking to undermine or overthrow something established)
* Heretical (holding beliefs contrary to established doctrine, especially religious)
* Unorthodox (not conforming to established norms)
* Scornful (showing contempt or disdain)
The best synonym for "irreverent" will depend on the specific context in which it is used.