They are living cosplays of the rivalry in the manga and just as stubborn as the characters themselves.
Occasionally, they put their differences aside and work together with the rest of the fanbase, just like how sometimes Zoro and Sanji team up for the benefit of the crew, but they can't help but revert to their true nature afterwards. They bait each other constantly and believe innocent bystanders are also involved in their dispute, just like Z&S. It's kind of fascinating from a distance.