I read a great analysis of this recently in the book "Playing Indian" by the historian Phil Deloria. I can't find the chapter online but I have a pdf copy if anyone wants to read it - I highly recommend it. This is my understanding of the argument:

The use of native-looking costumes by the colonists is drawing on long-standing traditions of both celebration and political dissent throughout European history. Going all the way back to ancient Rome and through the medieval era (probably starting way earlier, I would guess) the practice of inversion was common. So for example, during Saturnalia celebrations, medieval feast days, carnival/mardi gras and such, the servants would dress up as lords and the lords would wait on them. Or the kids of the household would tell the adults what to do, people would cross-dress, some random person dressed as a priest, etc. In some way a social norm or role was being reversed. Think of this happening while there are huge parties in the streets.

So on one hand, this practice of inversion - which you could find in one form or another in every culture’s celebrations (Halloween comes to mind) - fucks with the social order of the society, because you are switching roles of class/gender/religious role/etc which are usually very strictly enforced. At the same time you're also reinforcing the social order just by the fact that the inversion only happens at a very specific time for a very specific reason. Like "haha, isn't this ridiculous! it's totally backwards and strange and weird and would never normally happen without consequences!"

Okay so then the political dissent part. I’m not too familiar with this part of history but if anyone knows more I’d be interested to know. Basically, in England access to land and game was controlled by the landed nobility, and hunting by “common” folk was forbidden by the Game Laws. However, for centuries there was this kind of unofficial agreement between most nobles and the poachers, where if the latter would be discreet/reasonable in their hunting then the Game Laws wouldn’t be enforced against them. A key point here is that poachers practiced “blacking” as part of the discreetness thing - they paint their faces black and hunt at night to avoid being identified.

But then, after the English civil war the forests were owned more by the new rich, or essentially the bourgeoisie. They have an economic interest in profiting off the land rather than just a hereditary claim like the nobles, so they come down hard on poachers of any kind to protect those resources. As a way to resist this, the poachers start organizing and “blacking” together as a political act of protest. If a landowner was especially cruel in their enforcement of the Game Laws, groups of poachers would all get together in disguise and go vandalize the house or humiliate the owner in some way. This form of dissent was called “misrule,” btw, and it’s a tradition that gets carried over to the colonies.

Anyways, so basically what Deloria is getting at with this is that you have to understand both the traditions of inversion during celebrations and misrule as protest to understand the Boston Tea Party. Because the line between celebration and dissent is often blurred, and one could (and often did) switch to the other in any of these situations. You tend to think of the BTP as more strictly political, but the other commenter on this thread said they were probably drunk, so I think it fits.

Alright so applying this to the colonists in particular: Deloria (who is the son of the legendary native scholar/activist Vine Deloria, which I think is relevant) is using the Boston Tea Party to make a larger argument about the relationship between the English colonists and indigenous peoples. In order to protest against the Crown, the colonists had to adopt their own distinctive American identity to separate them from their British origins. By adopting a native identity, they're reinforcing their ties to the land that they’re occupying. To them being native represents freedom, seemingly endless land to explore and settle (and game, I might add), and basically everything boundless in opposition to the tight constraints of British land and society.

But there’s also a colonial racist element to this as well, because again, the practice of inversion is supposed to strengthen the division just as much as it challenges it. So while these dudes might dress up as native peoples in the night to destroy property, there’s an implication that they would never do something so savage and destructive in the light of day because they’re good and civilized colonials. Adopting this caricature of an “Indian” allows them to express themselves in ways that would be unbecoming to their everyday lives. The point is, "blacking" was considered a significant political act in itself and there are complex reasons that these colonists chose these costumes rather than just the standard disguise.

Plus, when it comes to actual encounters with native peoples, the colonists were waging a war on the frontiers and murdering/taking land, using all sorts of justifications like that they were managing the resources in a more efficient and civilized (European) way, unlike the "savages." So it’s this uneasy relationship where the colonists will identify with native peoples to protest the British, and then identify with the British to subjugate native peoples. And Deloria basically says that this contradiction is a key part of understanding the insecurities of the early American identity - and one that arguably is still playing out today.

TL;DR: The colonists dressed up in their interpretation of native attire to separate themselves from and oppose the British while reinforcing both their ties to the American continent and their authority over native peoples (in a more indirect way). It was both a political act and a disguise, which has precedent in English history as a political act in itself.