The phrase, "It is none of my business what others think of me," is geared to free people from the self-imposed prison of perception of 'Otherism' or codependency.
While it's true that 'what others think of me is none of my business,' it is also true that what I think of myself is none of my business.
"My" ONLY business is what God thinks of me; not even what I think of God is the point. My relationship with God is personal (God knows my name), but God's relationship with me is Eternal. God is the beginning and the end (may the Circle be unbroken).
I prefer to hear a person who says, 'my truth' means that they are not 'playing God' with their perception of the truth. It's akin to having confidence without conceit. In other words, no human is the ultimate authority on the facts. We grow along spiritual lines and are imperfect; we fall short of what we want to be and do. The Full Serenity Prayer illustrates this idea of *trust over human comprehension:
God, grant me the serenity to accept the things I cannot change, Courage to change the things I can, and wisdom to know the difference. Living one day at a time, enjoying one moment at a time, accepting hardships as the pathway to peace, taking, as He did, this sinful world as it is, not as I would have it. *Trusting that He will make all things right If I surrender to His Will so I may be reasonably happy in this life and supremely happy with Him Forever and ever in the next. Amen. (prayer attributed to Reinhold Neibuhr, 1892-1971).
I agree that there is not my or your or anyone else's truth. Truth ain't a democracy; it also isn't a theocracy (personal freedom to worship or not keeps us all free), but Jesus said 'the TRUTH' will set [us] free [from ourselves]. No truth rises above the audience's mind short of a miracle. The Day of Pentecost is an excellent example of divine proof. No one who experienced the Holy Spirit's power that day found themselves limited by the constraints of their linguistic heritage, societal prejudices, and incorrect teachings.
Ask a stupid question and get a stupid answer. When Pontius Pilot asked Christ, "What is truth?" what was Jesus's response?
Truth without compassion is cruelty. “…but speaking the truth in love…”is imperative. Beating people up with the 'truth' is reprehensible. Measuring out the truth (as wisely as a serpent) is a maturity that doesn't require diluting truth. Thou shalt not lie doesn't mean we puke out the truth on people. Agreeing with the adversary while we are in the way is not lying, is it? Are we telling the truth when we cast pearls before swine? Yes, the truth is the truth, but who among us pushes people away from Christ under the disguise of 'well, it's the truth! You can't handle the truth!"
We don't hide the truth under a bushel, but we can shine so that those with eyes to see and ears to hear will discern the truth. Before speaking, pray. I can say everything wrong; my arguments might be insufficient to win a debate, but because I pray, God will help someone hear it right. It's not all about me.
Milk before meat.