EXCLUSIVE

Scott Baio's alleged attacker's not only facing a Sheriff's investigation -- she's also dealing with a school full of angry parents demanding the school drop the hammer on her.

Sources close to the situation tell TMZ ... Nancy Mack, wife of Red Hot Chili Peppers drummer Chad Smith, could be looking at a possible ban from all school functions after she went off on Scott for supporting Donald Trump.

We're told parents were livid and filed complaints with school officials. We broke the story ... Scott told cops Nancy continually shouted, "Grab 'em by the pussy" while making a scene at their kids' elementary school event.

An official at the private school wouldn't say what, if any, punitive action it would take against Mack ... but said, "Our highest priority is the safety and privacy of our children and their families."

There's some irony here too -- the alleged physical confrontation between Nancy and Scott went down at a school play where students said "Merry Christmas" in more than 10 languages.