The gemara (Sanhedrin 59b) writes that the mitzvah of milah was not given to all bnei noach, but only to Avraham and his descendants. The gemara has a miyut to exclude Yishmael and Eisav from the chiyuv, but darshens the extra words אֶת־בְּרִיתִ֖י הֵפַֽר (17:14) as a ribuy to include the children of Keturah.
Rashi and Rambam disagree as to the scope of the chiyuv. Rashi comments לרבות בני קטורה. אותם ששה לבדם ולא זרעם אבל אברהם נצטווה לכל הנולדים לו that it only the direct children of Keturah who are chayav in milah, but not their descendents. The Rambam, however, paskens (Hil Melachim 10:8)
אמרו חכמים שבני קטורה שהם זרעו של אברהם שבא אחר ישמעאל ויצחק חייבין במילה. והואיל ונתערבו היום בני ישמעאל בבני קטורה יתחייבו הכל במילה בשמיני. ואין נהרגין עליה.
Since the Rambam speaks about the chiyuv for bnei Keturah b'zman ha'zeh, we see that he holds all future descendants of Keturah, not just the first generation, are chayav.
Earlier this week R' Avraham Erlanger, R"Y of Kol Torah and author of the Birchas Avraham series on various masechtot, passed away at age 90. Whenever I look at the B"A I am always taken by its clarity and the neat way he is able to boil down complex ideas into neat formulations. He was a master of lomdus.
He poses the following chakira on this din: is the chiyuv for bnei Keturah an extension of the same chiyuv milah that was given to Avraham and his children, or is it a new din, a new chiyuv?
Nafka minah: the Achronim (Pitchei Teshuvah YD 264:5) debate according to the Rambam who holds all descendents of bnei Keturah are chayav whether they can be mal a Jewish baby. R' Elanger suggests that this issue may depend on his chakirah. If the chiyuv for bnei Keturah is a new din, then just like an aku"m cannot be mal because they are not included in the command of וְאַתָּ֖ה אֶת־בְּרִיתִ֣י תִשְׁמֹ֑ר given to Avraham, so too bnei Keturah. But if the chiyuv for bnei Keturah is an extension of the mitzvah given to Avraham, then they are included in whatever command he was given.
Not mentioned by the Birchas Avraham is the very strange comment of Ramban on Devarim (2:4) אֲחֵיכֶ֣ם בְּנֵי־עֵשָׂ֔ו:
טעם אחיכם בני עשו – שיחוס ישראל מן אברהם, וכל זרעו אחים, כי כולם נמולים. וזה טעם: לא תתעב אדומי כי אחיך הוא (דברים כ״ג:ח׳). רק בני הפילגשים, ישמעאל ומדין וכל בני קטורה, אינם באחוה מן הכתוב: כי ביצחק יקרא לך זרע
According to Ramban, the descendants of Eisav are called our brothers because they have a milah, as opposed to the descendants of the bnei pilagshim, i.e. Ketuah, who don't.
The exact opposite is true! Bnei Eisav have no chiyuv milah; bnei Keturah do.
Whatever the pshat with respect to his comment re: bnei Eisav is, we can at least salvage the line about bnei Keturah with the Birchas Avraham's chakira. The descendants of Keturah are chayav in milah, but that is not the same chiyuv as our chiyuv; therefore they do not share a bond of achvah with us. (See Chemdas Yisrael p 112)