The Mishnah (Avos 4:3) quotes Ben Azzai as saying:
Do not insult any man and do not dismiss anything, for there is no man who does not have his day and there is no thing that does not have its place.It is telling that the Mishnah uses the phrase "kol adam -- any man." Rashi explains that this is to teach us not to insult "any man in the world," which I think clearly includes Gentiles and non-religious Jews.
While the Mishnah seems to imply that this admonishment is based on a utilitarian reason -- certainly no small concern -- the Tiferes Yisrael offers a different explanation:
Do not insult any man -- even a fool, a simple man and someone mindless, and even if he is a wicked man who is sentenced to death. Pity their ruined state and do not insult them because you are only offending their Creator. Even if you do not know why they exist, God understands his ways: "The Lord has made everything for its purpose, even the wicked for the day of trouble" (Prov. 16:4).