Judge Judy is so rude because the TV show Judge Judy really is just that a TV show and not a real court room like in a regular court proceeding.
Judge Judy is just an arbitrator and does not have any real powers as a judge and so she can be rude as part of the TV show for entertainment.
The reason people really watch that old hag Judge Judy is because of the rudeness she does to people in her TV show court room.
Have noticed the bailiff doesn't carry anything on them such as a duty belt etc?
That means that the Judge Judy Bailiff is just there for entertainment as well and he's not a real law enforcement officer or Bailiff and they would have to call the police to come and arrest someone.
Judge Judy is not a real judge anymore although she used too be and I cannot find anything interesting in the Judge Judy Show.