Authenticity in philosophy is not generally about cultural expressions, but about being true to yourself, about acting in ways that relate authentically to who you are.
I argue wisdom is about a practice, to be able to act from the integrated centre of pur concerns, not impulsively or hesitantly, not in ways we are likely regret, and according to our values. More on that here: Wisdom and John Vervaeke's awakening from the meaning crises?
So in this sense, wanting someone to be authentic, to be wise, is wanting the best for them, for their true self, their integrated self. If someone feels they have to live a lie, you know they will be sorry, that they will waste opportunities for joy, and completeness.
You seem really just to be asking about cultural appropriation. What is authentic is not in ways of acting, or artifacts. What is authentic, what is wise, is about intentions.
For years Native American war bonnets were used as a shorthand for 'savages', for games of cowboys and Indians to represent the 'baddies'. So everybody, including the former Washington Redskins team realised, this is not cool any more.
But people have got outraged over white people wearing kimonos. Even when they are gifts from the Japanese government, or when almost all Japanese people are happy to see anyone wear them. Why is it different to Japanese people wearing a suit? They weren't oppressed and dismissed as savages, quite the opposite, they did those things in WW2. Is it 'authentic' for a white person to wear a kimono? That's inside them, it's in their motivations.
To want others to be authentically themselves, is to want what's best for them, from the integrated centre of their concerns.