Where did the idiom 'crossed the line' originate?

It probably came from trade unions. They would go on strike and form a line outside their workplace. Those who sided with management rather than labor would cross through that line. So crossing the picket line symbolically meant to support whatever practices those on strike found abusive.

Another image that comes to mind are the cities of refuge in Old Testament Bible times. Cities of refuge were places for people who committed certain types of crimes such as involuntary manslaughter or were involved in an accidental death. As long as they stayed within the boundaries of the refuge cities, they were legally protected from retaliation. But if either party, whether the accused or the family of the victim, were to cross that boundary, there would likely be trouble. If the accused left the refuge city, then the family would be legally allowed to seek vengeance. If the family of a victim were to cross into a city of refuge and kill the person, then they would face capital punishment. The exception would be if someone killed in cold blood in the first place and falsely claimed the right to refuge. Then any blood avengers would likely be cleared for taking out the deliberate killer.