You only have to answer to yourself
When it comes to authenticity, there's only one person that you have to answer to --- YOU. And only you.
The concept of authenticity is about being true to you - be you - because if one is not living in alignment with one's true nature, it causes internal conflict and struggle. For example, if your true nature is to create musical notes that would move the World but you are holding a surgical knife and cutting bodies up because it makes more economical sense to do so, it will cause internal conflict and struggle.
It is not about how you present yourself to the World. You can (although you shouldn't) lie to the whole world but there's only one person you can't lie to --- YOU.
As long as you are living a life that is true to your nature, you are being authentic and there is no need to prove to anyone else.
You've gotta look beyond the superficial
When I hear people saying, "They tell me to be myself so I speak my mind but when I do that, people don't like me", I know they got authenticity wrong.
Some may even feel guilty when they behave other than what they're currently feeling eg. pretending to laugh when in fact they are not amused or putting on a strong front when they are feeling miserable inside.
They got authenticity wrong.
When it comes to authenticity, only the important things matter i.e. your values and beliefs, and personality and talents. Because these are what make you, you - the idiosyncratic you.
And what matter isn't the apparent but the underlying...
Speaking your mind doesn't make you authentic because as mentioned above, it is about your values and beliefs, and personality and talents, not your expressions.