An Anti-Union is a Union that aims to destroy other Unions and organizations. For example, an Anti-Union might crash another Union's events and flame/spam their thread until that Union gives up. An Anti-Union might also declare war on any Union/clan/organization that is not allied to them.
Some Anti-Unions will send a person to crash their clan chat with spam.
Anti-Unions normaly don't last long, as not many people wish to join them and action can be taken against them.
At least one Anti-Union has caused enough trouble for Jagex to take notice. It still exists off of the official game forums to this day.