Is insulting "Abu Lahyah" considered apostasy from the religion, knowing that the one who said it has reconciled with the other party?

Your saying to your Muslim brother, who adheres to the Sunnah (definition), "Abu Lihya" (Beard-man) is a grave sin, because you are mocking, ridiculing, slandering, and taunting a Muslim for a Sunnah from the Sunan of Fitra (primordial nature), an obligation from the obligations of the religion, and a شعيرة (ritual/emblem) from the شعائر of faith. This is counted among the major sins. If your intention was to mock the Sunnah of the beard, then this is one of the nullifiers of faith, and necessitates ghusl (definition) and repentance. If your intention was to mock the person himself, then this is a major sin that requires repentance. In both cases, you must apologize and ask for his forgiveness.