In TOS Space Seed, Lt. Marla McGivers identifies Khan Noonien Singh as a Sikh.
(Looking at Khan) From the northern India area, I'd guess. Probably a Sikh. They were the most fantastic warriors.
Lt. McGivers' assessment is supported with Khan's last name being Singh, which is strongly associated with ethnic Sikhs and at one point was mandated for all baptized men.
Sikhs are also traditionally followers of Sikhism, a religion in which one of its tenets is Kesh, the practice of growing out one's beard naturally. Guru Gobind Singh Ji explained this reason, noting in particular facial hair.
My Sikh shall not use the razor. For him the use of razor or shaving the chin shall be as sinful as incest. For the Khalsa such a symbol is prescribed so that his Sikhs can be classified as pure.
Does the fact that Khan is clean-shaven, in violation of Kesh, indicate that he is not a follower of Sikhism despite being an ethnic Sikh?
I'm open to answers from any level of canon.