This is a question about etiquette, and as a firm believer that much communication is non-verbal I am happy to try and answer this, as our choice of dress does communicate a message to others which may or may not be well received.
By way of disclaimer, this answer deliberately avoids any discussion of "cultural misappropriation" or racism which are not topics for here.
If you asked most people in the western world what a man should wear to a job interview they would answer "a suit". This is because a suit is traditionally national dress for a man in countries such as the UK or the USA. What actually constitutes a "smart suit" of course changes over time with shifts in trends, for example different styles of shirt and tie coming and and going from fashion.
Most generations would agree that where a person has a different cultural heritage, their equivalent "national dress" is equally appropriate in a formal setting. For example in the UK many with Scottish ancestry like to wear kilts at weddings; likewise I would expect to see people with Indian heritage wearing Dhotis and Saris to such occasions in the UK. These forms of dress are considered smart within those cultures and so are perfectly acceptable.
As to people wearing the national dress of a culture to which they have no ancestral claim - well, using the examples above I can say that if the groom at a wedding was wearing a kilt then often the rest of the wedding party will do the same irregardless of their own heritage. I have also observed white British women wearing Saris when attending an Indian wedding. How this is perceived by others will surely vary but this is not a debate for IPS.
If you are considering wearing a dress that would normally represent another culture, you need to consider who will see it and how they might perceive it - will they see it as a respectful homage, a tasteful personal fashion choice, or an insult to their heritage? Only you can decide that.
A good benchmark may be the example I gave before - a job interview. When you attend a job interview you want to give a good impression, and in most cases you do not know the people that will be conducting your interview. Ask yourself - would I wear this to a job interview? If the answer is no, out of concern that you might give a bad impression or send a wrong message, or perhaps even insult someone's nationality or heritage, then perhaps you would be best not wearing it to a public function either. If on the other hand the event you are attending is more exclusive where you know most people and can perhaps anticipate their reactions, you may be able to express yourself more freely through your fashion choices.
