"I can't change. This is just the way I am. I need to be true to myself."
There is actually some truth the above statements. We do behave according to our true nature. This is a part of what the Apostle John is trying to get us to understand in his first epistle. "...you know that everyone who does what is right (righteous) has been born of Him (God) (1 John 2:29)." "He who does what is sinful is of the devil...(1 John 3:8a)".
This is why who we are must change! This is why we need to be born again. In our natural birth, we are born into a life of sin. It's not so much that we do sin, but it is actually a part of our nature - we are born with a sin nature. And, therefore, the inheritance we receive comes from the father of sin - the Devil. Our destiny is his destiny. It is a life in the bondage of sin and an eternal death.
Now the good news is that we can receive new birth. We can be born again because Jesus defeated Satan, sin and death on the cross. And when we receive this new birth, we receive a new nature. We become "new creations". We don't just add Jesus to our life, but we become an all together different person on the inside with new desires and motivations. And our inheritance changes because we now have a new Father. It is an inheritance of freedom and eternal life. "No eye has seen, no ear has heard, no mind has conceived what God has prepared for those who love Him." - praise God!
So, yeah, in sense we must be true to who we really are. That is why who we are needs to change. And God offers the world new life and we receive it when we trust Him.
And the appeal to those of us who are children of God is to be true to our identity. That is, "to walk in the light as He is in the light (1 John 1:7)". See sin and Christ for who they are - one a destroyer of our lives and the other the Savior of our lives. So when sin creeps up in our lives (and it will), see sin for what it is (destructive) and repent and receive forgiveness.
God is good!