Bnei Yishmael and Bnei Keturah:[1] Some Poskim[2] rule that although the descendants of Yishamel are not obligated in the command of circumcision, nonetheless, the descendants of Ketura are obligated in circumcision being that they are descendants of Abraham who were born after he was commanded to circumcise himself and his offspring, and this command applies eternally for all generations towards his descendants who were born from that time and onwards. Accordingly, they rule that since historically the descendants of Yishmael became intermingled with the descendants of Ketura, that therefore it is an obligation to circumcise all descendants of Yishmael, as perhaps they are in truth a descendent of Ketura. According to this opinion, it is not only allowed but even a Mitzvah to circumcise a Gentile who comes from the lands of Yishmael. Accordingly, a Jew may perform circumcisions on Muslim boys when they reach 13 years of age.[3] However, other Poskim[4] rule that in truth the descendants of neither Yishmael or Ketura were ever obligated to be circumcised, and hence it is forbidden for a Jew to circumcise a Muslim due to the above prohibition against circumcising a Gentile. Practically, the main opinion follows this latter approach.[5]

[1] See Shagas Aryeh 49; Pischei Teshuvah 263:14; See Pesakim Uteshuvos 263:11 footnotes 84-85; See Encyclopedia Talmudit Vol. 46 Erech Mila p. 401-402 footnotes 24-32

[2] Rambam Hilchos Melachim 10:8

[3] Shagas Aryeh ibid

The reason we do not follow the majority population: Although Sancheirev mixed all the nations with each other and it is hence found that there is no country with a majority Bnei Ketura population, nonetheless, we do not argue that we should follow the majority regarding the circumcision obligation of Bnei Ketura, and on the contrary we say that everyone in the country is obligated to be circumcised due to the minority of Bnei Ketura that is mixed within them. The reason for this is because the rule of following the majority only applies to the Jewish people, and does not apply towards Gentiles by which one must be stringent to follow even the minority. [Noda Beyehuda Tinyana E.H. 72 in answer to the question of the Shagas Aryeh ibid against the Rambam; Peri Megadim Reish Shaar Hataruvos Chakira 3; Pischei Teshuvah 263:14] Alternatively, the reason that we do not follow the majority by the Gentile population of a country, is because there always remains a minority of the indigenous people in their land. Thus, there are certainly some descendants of the original Bnei Ketura from Biblical times who currently live in lands of Yishmael and these indigenous Bnei Ketura have the status of Kavua. [See Levush E.H. 4; Likkutei Sichos Parshas Shoftim Vol. 19 Sicha 2]

[4] Rashi ibid

[5] Shagas Aryeh ibid

The reason we do not follow the majority population: As aside for the fact that the main opinion follows that of Rashi that Bnei Ketura are not obligated in circumcision, furthermore, even according the opinion of the Rambam, ever since Sancheirev mixed all the nations with each other there no longer exists any country with a majority Bnei Ketura population, and since the Torah holds that one is to follow the majority, therefore there is no longer any circumcision obligation on any Gentile. [Shagas Aryeh ibid, brought in Pischei Teshuvah ibid]