Shia LaBeouf Arrest

Shia LaBeouf's arrest and heated exchanges with protesters aren't scaring off the museum hosting his web cam ... but it has a warning for the actor.

A rep for The Museum of the Moving Image says they consider the protest site more of an art exhibit -- and they expect people who show up there to act with common decency and respect, and that means not assaulting visitors. That goes for Shia, too. We're told the museum will continue to monitor the live stream.

As we reported, NYPD cops busted Shia early Thursday morning after he allegedly got physical and scratched a guy in the face.

The museum's sticking to the plan to run the live stream through President Trump's term.

Shia LaBeouf was arrested in Austin, Texas Thursday ... and witnesses say the actor was blitzed, out of control and disobeyed police.

Shia was taken to the Travis County Jail and booked for misdemeanor public intoxication.

It happened at around 7:45 PM CT outside a bar on 6th Street. A witness says Shia was either extremely drunk or high on drugs when he ran down the street and jaywalked in front of police. They warned him not to do it but he continued, acting bizarrely.

Cops subdued him and put him in cuffs.

Another witness tells us, before the arrest Shia and a woman tried walking into a bar but they were denied because they were too intoxicated. Shia began swearing up a storm and tried forcing himself into the bar but was blocked. Shia and the woman left and began walking.

Shia, who's been to rehab, has been dogged by substance abuse problems. He had a similar situation in NYC last year, where he was arrested after acting crazy at a Broadway play.

He's in town for the Austin City Limits music festival.