The distinction of Hawaiian in reference to native people is a only made off the islands. To anyone from Hawaii or familiar with it calling it a Hawaiian shirt literally is wrong in our understanding of the word.
To try and spread that understanding of Hawaiian as reference to native peoples is to spread the knowledge that Hawaii is a multiethnic place with distinct native culture alongside its American, Asian and other Polynesian influences.
Well, 8 billion people live outside the islands. Their use of the word will prevail for an object that's available everywhere in the world.
The AP's style guide uses Hawaiian as an adjective.
It is a messy thing when typical ways of speaking English conflict with nuances.
And additionally better isn't always the most succinct. I use Hawaii resident or kamaaina to say I'm from Hawaii, I don't call myself Hawaiian.
The person I first responded to called the shirt 'as genuinely Hawaiian...', which while true to describe its geographic origin, carries a different connotation. I think I made that point clear.
I don't think we'll get too much more understanding arguing points of grammar, you have a fair point with using Hawaiian as adjective. Thanks for the discussion.