Theres a big difference between expressing ones opinion and going on youtube and making an outright fool of yourself and doing nothing for the cause your "supporting" other than making us all look like foul mouthed anger management candidates. Folks get fired for their foolish actions online all the time. Any job that deals with the public is going to look down on you publically making an ass out of yourself.
Sounds like maybe he has been involved in shenanigans before and this was the last straw. Anybody with a brain has to realize that you can't go on youtube posting videos like that and expect not to get in trouble especially if the you're a public employee.