In a recent television program, this scenario of "please remove your head covering before I'll accept you as a person" is acted out humorously, as a man who has gone deeper into his Jewish spirituality has begun wearing a yarmulke, and is not going to be allowed to enter a restaurant wearing it. It's a Palestinian chicken restaurant, which makes this a scene from a comedy, of course, but fantasy does tend to reflect reality, and in this case, according to the writer, Larry David, it does so purposely. The show is "Curb Your Enthusiasm", and a clip of the video is linked to the article.
Paragraph of note:
"Leo Rosten claims that the word "yarmulke" comes from the Tatar word for skullcap. However, I think it's more likely from the Aramaic "yira malka" meaning "awe of the king" as a sign of respect to God. Whatever one's reason for wearing a yarmulke, they deserve to be treated with respect. Whether you're an Italian New Yorker experimenting with many religions or a spiritually renewed Jewish dentist going to eat some Middle Eastern chicken."