The nationality aspect is really key here. It's not particularly weird to have a sci-fi or fantasy setting where some people have an indigenous-feeling style, like Horizon: Zero Dawn or Enslaved: Odyssey to the West (just off the top of my head), and while there might be some questions about how and when that's handled well, people are generally gonna be okay with it.
The issue here is that it's a fantasy world -- not Earth, but a place with its own different cultures -- but the character is just a pastiche of Native American stereotypes, and especially the feather headdress which is a specific tradition of Plains tribes and seen as religiously and culturally significant. On this level it would already be pretty weird to include any class that was really heavily tied to a specific real-world ethnicity that doesn't exist in BD's world, but you add that to the current situation of indigenous Americans (who, unlike Spaniards or Brazilians, don't have a country and a large population to maintain their cultural traditions) and it gets really ugly to just exploit these people's imagery without any context or respectfulness. It's not a completely unique situation, but it is one specific to indigenous cultures that have been mostly wiped out and therefore don't have the same ability to influence the use of their culture as people with a current national identity do.
EDIT: A few of the original BD classes have outfits that are inspired by ethnicities -- the Spell Fencer by an Arabian style, Monk by China, etc. -- though they're all a bit more of "inspired by" than directly imitating. I honestly think if this class hadn't had the feather (which has a specific significance) and had a better name instead of "Tomahawk" (which honestly is the most offensive part) nobody would've given it a second look. Even then it wasn't changed because people complained, but rather affirmatively changed by localization staff who recognized how issues of Native American representation have been common in media the last few years and wanted to avoid a tone-deaf choice.
