I guess where I draw the line is when things get personal. Criticism for the job done is par for the course, and demonstrations are fine if you feel like you want to do it, but I don't feel comfortable calling people names or worse, threatening the person or his family.
Soccer fans are a hardcore lot. I recall Liverpool fans going out on the street demanding that gillette and Hicks surrender the team. Fine, but I also recall him talking about personal threats, which is just unacceptable.
It is possible to voice your displeasure about an organization without resorting to the personal route.