May one take a haircut, shave or cut his nails on Rosh Chodesh?
Rabbi Yehuda Ha'chasid (Germany, 1150-1217) writes that one should refrain from these activities on Rosh Chodesh. Later scholars understood that he applied this ruling even when Rosh Chodesh occurs on Erev Shabbat, and held that one should not cut his hair, shave or cut his nails on Rosh Chodesh even in preparation for Shabbat.
The question, however, arises as to whether the Sepharadim have accepted this position as authoritative. Chacham Bentzion Abba Shaul (Jerusalem, 1924-1998), in his work Or Le'tziyon (vol. 3), observes that Sepharadim have the custom of allowing nail-cutting on Rosh Chodesh. Regarding shaving and haircutting, too, it appears that the Sepharadim did not accept Rabbi Yehuda Ha'chasid's ruling. The Radbaz (Rabbi David Ben Zimra, Egypt-Israel, 1480-1574) observes a custom to take haircuts on Rosh Chodesh Iyyar, clearly indicating that haircutting is permitted on Rosh Chodesh. So although the Chida (Rav Chayim Yosef David Azulai, 1724-1806) observed a number of Rabbis who indeed made a point of observing the stringency of Rabbi Yehuda Ha'chasid, it seems that the general custom is to be lenient in this regard.
This is indeed the ruling of Chacham Bentzion Abba Shaul for Sephardim, that one may cut nails, cut hair and shave on Rosh Chodesh, unless he has a particular custom to refrain from doing so.
