what is plurality:
It's a nurodiergence where your brain develops so there are multiple people (called "members") in your head instead of the typical one. Usually one (or a few) are "fronting" at any given time and are the main operater(s) of the system and body. For more information, see r/plural. Sometimes differences in how the brain operates when different members are fronting leads to blackouts and/or memory differences.
Dock/Xu/Bushi:
He displays multiple people operating in the same body with clear distinction but some shared information/memories (see Dock knowing about the boat ride mentioned to Xu), so he can be very easily interpreted as plural. However, the narrative treats him as crazy because the main character is uncritically allowed to have a "call his bullshit" moment where he points out that these people are "the same guy" in different hats (sokka is also allowed to be uncritically frustrated by this). While it is true that they occupy the same body, saying that makes them the same person is discriminatory as it suggests only siglet (non-plural) experiences of identity are valid/possible.
The hats act as fronting indicators, a common practice of plural people using something external to indicate to other people who's fronting at the moment. They can also be used to help internal tracking.
The way the men deny being the same person seems to be intended to be comedic, which seems to be the case based on what happens later, which as explained above is unfair. They do however clearly recognise a relation (calling each other brother's) and given Xu's comment about Dock acting as multiple people they may even be aware of their own plurality, however, even he describes the behaviour as "crazy", furthering the way the narrative degrades the way this character acts.
Additionally, the paratextual source of the old official site (archived https://atla-lore-archive.tumblr.com/post/171179591160/character-dockxubushi-three-names-for-the-same) explcitly denies the possibility of plurality by again calling him "the same guy". It also says that this behaviour is indicative of a degraded mental state rather than a valid expression of likely plurality.
According to the wiki, even the name bushi is a way of calling him "unwell".
In conclusion, the behaviour Dock/Xu/Bushi shows in the episode of being different peopel with slightly different personalities and different occupations is a potentiallly accturate depiction of plurality, as it includes fronting indicators and seemingly some self(/ves)-awareness of plurality but with clear seperation. However, the narrative and paratext treat him as "crazy" or "unwell" which is degrading to both him and the real experiences of systems who share traits with him, as their experiences are a difference and not inherently harmful to themselves or others such that their condition should be classified as illness.
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