Tenderness of heart is being sensitive to God’s touch. Therein, discernment is necessary and discipleship too so that we know it is God Who is touching us and that in accordance with His Word.
I have known many who are so sensitive to their conscience that even after they repented multiple times for the same iniquities they give up hope. Their wound was much too large to them for God to heal and there was no balm in Gilead. That is not the God of the Word; the Father of our Lord. He sent us a Savior just as tender and if we only took to heart what was written, “A bruised reed He will not break,” then we would know God’s touch and rejoice.