First of all, shiraglassman, sorry for taking so long to answer! The beginning of Passover wiped me out.
It’s a good question… To be honest, I’m not really sure what would or would not give someone ‘the right’ to wear a hamsa. It’s not a symbol that belongs to any particular place or tradition. At the same time, from a historical perspective, it’s true that the hamsa was a prominent artistic element in Jewish art from North Africa, the Mediterranean, and Central Asia, but was not used in the Ashkenazi community until the last 50 years or so. As shown in Sabar’s essay on the Jewish history of the hamsa, in Israeli society the hamsa has been transformed into a general symbol of ‘Israeliness’ and ‘Mediterraneanness’ and in particular a symbol that is distinctly disconnected from religious and nationalist narratives, unlike the “Jewish star” (something also noticed by Alexandra Nocke). It’s not a coincidence that the hamsa appears in the logo for almost every peace initiative, alternative Israel tour, Arab-Jewish coexistence project, etc.
Is it a Jewish symbol? Definitely (well, as much as anything is a Jewish symbol). Its historical origins are unclear, but the idea of a hand as a protective symbol goes far back into antiquity. We know that the hamsa symbol was widespread among both Jews and Muslims already in the Middle Ages, and by then it had taken on different symbolic associations for the different communities — for Muslims, the “five” of the hand relates to the Five Pillars of Islam and to the five members of the Prophet’s family, the Ahl al-Bayt, while for Jews, the “five” of the hand relates to the significance of the fifth Hebrew letter “heh” as a symbol of the Divine Name as well as the iconographic importance of the outstretched hands of the Priestly Blessing (birkat kohanim).
Should Ashkenazim wear it? Well, it depends on how you feel about the relationship between different Jewish groups. Many “Jewish” customs originated in one specific group — for example, wearing costumes for Purim is originally an Italian Jewish custom; smashing a glass at weddings is originally a German Jewish custom; throwing candies at a bar/bat mitzvah is originally a Sephardi Jewish custom; etc. etc. With regards to the hamsa, while it did not originate in Ashkenaz, its symbolic associations (divine protection, blessing, warding off the evil eye) are all consistent with Jewish culture in general, and there is nothing that ties it to one specific community — it is not a symbol of “Moroccanness” or “Persianness” or anything like that. At the same, I can understand why some people might be reluctant to erase its non-Ashkenazi history. I wear it myself, and I appreciate it as a Jewish symbol shared with Muslims and not tied to the State of Israel, but I acknowledge its origins as elsewhere to my own family’s heritage. Ultimately this is my opinion, and feel free to disagree!