After the terrorist attack in Paris and the drastic rise in anti-Semitic incidents in France, an Israeli from Rechovot invented a Kippah from human hair. The Kippah is camouflaged within one's hair so that anti-Semites will be unable to identify a religious Jew, and yet one will still be covering his head. Is this permissible?
Three questions arise regarding this issue: 1. Is wearing a Kippah an actual obligation? 2. Does the Halachah permit a Kippah made from hair? 3. Is hiding one's Kippah considered hiding his Jewish identity, something which was forbidden in the past during times of anti-Semitic and anti-Jewish decrees?
1. A Kippah is an absolute obligation. A Kippah is of great importance. Our Sages explain that a Kippah is meant to instill fear of Hashem within us and is a sign that the Master of the Universe is above us (Shabbat 156b. Kitzur Shulchan Aruch 3:6). According to the Achronim, it is even more of an obligation in our times, since wearing a Kippah has been accepted by Torah observant people (Shut Meharshal #72. Shulchan Aruch Ha-Rav 2:6 based on accepted Jewish practice. And some say not wearing a Kippah is imitating non-Jewish practice. Shut Chatam Sofer, Choshen Mishpat #191).
2. A Kippah made from hair is nothing new, since there have always been toupees. The Mishnah Berurah (2:12) already brings a dispute as to whether a toupee is considered a Kippah. Some forbid wearing a toupee without a Kippah on account of Maarit Ayin (This is also the opinion of Ha-Rav Yaakov Kamenetzky. Emet Le-Yaakov on the Shulchan Aruch ibid.). This is the ruling of the halachic authorities, such as the Sedei Chemed (Maarechet Kaf, Erech Kippah), that one needs a recognizable Kippah.
By the way, there is criticism in our times against wearing a small Kippah which cannot be readily seen. According to Ha-Rav Ovadiah Yosef: “It should be recognizable and visible from all sides of the head, front and back” (Shut Yehaveh Da’at 4:1). And according to Ha-Rav Moshe Feinstein, it is best to cover the majority of one’s head (Shut Igrot Moshe, Orach Chaim 1:8).
Nonetheless, in a pressing circumstance, it is permissible to cover one's head with a toupee (see Mishnah Berurah ibid.). This is on condition that the Rabbis in France permit it, since we cannot decide on something which occurs there, as Ha-Rav Moshe Feinstein stated: The Rabbi from Minsk should not interfere in questions of the Rabbi from Pinsk (Meged Givot Olam Volume 1, p. 55. Volume 2, pp. 31-32).
There is also an alternative solution, which is to wear a hat that is not unique to Jews (Piskei Teshuvot 2 note #57).
3. It is true that if one is asked if he is a Jew, it is forbidden for him to say that he is a non-Jew. But the Shulchan Aruch (Yoreh Deah 157:2) already permits one to wear non-Jewish clothing so as to appear as a non-Jew, on condition that he not declare that he is a non-Jew (Regarding this question during the Holocuast, see Shut Mi-Maamakim of Ha-Rav Ephraim Oshry 1:15, 4:12, 5:3).
It is therefore permissible to wear a "Hair Kippah" but it is preferable to wear a hat.
And there is obviously an even greater solution: Making Aliyah. Here, in Eretz Yisrael, one can proudly wear a Kippah.