The safest response is to send as short and clear a letter as possible. Do not avoid taking blame. Write something along the lines of: "I am sorry. I try hard, but am not perfect. While what I said in the sermon (Bible class, our conversation, whatever) was God's own truth, I am sincerely sorry that I said it in a way that offended you. It is my only desire that you know the love of God in Christ Jesus. Please forgive me. I am still learning and struggling to be faithful to God's Word in service to His people."

That is the pious response to a vicious attack. A letter is safer than a phone call or meeting because you can choose your words carefully. It is good to get into the habit of letter and note writing. Keep copies of all angry letters and your replies. If you have a board of elders, consider showing them both.

Finally, let go of it. It is not your fault. You didn't do anything wrong. People are offended by the Truth and you're God's man in that place, so they come after you. They know Incarnational Theology better than they think. Of course, they think God is on their side. Their god is. That is why they attack. And that is why you suffer. It is the character of your respective gods. Your God suffers the violence of theirs and He does it in you.

Let that help you sleep but don't dwell on it much. Instead, love your enemies. Discipline yourself to embody the pious, humble character of your "apology" letter as much as possible. Let them off the hook for free, forgive them without cost or demand or strings. Be the Gospel to them and pray for them.