How is that allowed in a royal household? Maybe her parents did not expect anyone to steal away with their daughter. As a matter of fact, even though the crown was poorly guarded, it had more guards than Rapunzel did. Mother Gothel, by no means a spry woman, was able to scale the wall to Rapunzel's room and climb in through the window.
Just look at how well Rapunzel was guarded, i.e. Honestly, I'm not surprised that Rider was able to get away with the goods. He was lowered down from the ceiling while all the guards were looking at the front door. There were a good amount of guards protecting the crown from theft, but not a single one of them was looking towards the crown when it got stolen. We get our first good look at what the guards are like at the castle when Flynn Rider steals the crown right out from under them.