A situation that would seemingly force me to choose between being right and being kind would be similar to Job's, as he faced accusations from his friends. Job's friends became falsely convinced he had a secret sin, and each admonished him with misapplied truth. If I found myself in such a dilemma, I would prioritize being right just as Job did.
God forbid that I should justify you: till I die I will not remove mine integrity from me. My righteousness I hold fast, and will not let it go: my heart shall not reproach me so long as I live. Job 27:5-6
Being right puts me on the side of God. A very beautiful verse, Job 35:10 reads: "...Where is God my maker, who giveth songs in the night". Knowing that you and God are right is the path to victory. No matter what your friends say, you know you have a "song in the night" because God's spirit has made you righteous.
Further analysis of Job’s dialog with his friends reveals that he was not at all unkind. However, he did use emphatic statements to persuade his friends that their conclusion was wrong. The result was that with God's help, Job's friends eventually recognized the truth, and their friendship with Job once again flourished.
And the LORD turned the captivity of Job, when he prayed for his friends: also the LORD gave Job twice as much as he had before. Job 42:10