What is the view of the Noachide movement on bris milah for non-Jews descended from Abraham?

Question

The Noachide movement is a movement that encourages non-Jews to follow the Seven Noahide laws---that is, the Mitzvot that are binding on Noach and his descendents (in other words, on all living humans). An apparently-typical statement from the movement would be the following (from here):

According to Jewish teaching, the Torah of Moses contains a covenant (given at Mt Sinai) binding on the Jewish people consisting of 613 commandments, and another known as the ‘Covenant of Noah’ consisting of seven commandments which is binding on all the peoples of the world who are not Jewish.

See here for more information on the movement. (It seems that the Rambam was of the opinion that Jews were obligated to try to encourage gentiles to follow the Noahide laws; this was very much a minority opinion among the sages but the contemporary Chasidic movement seems fairly well-disposed to Noahidism.)

My question is the following. When spreading awareness of the Noahide laws amongst B'nei Noach, one might think it should be equally important to spread knowledge of Bris Milah amongst B'nei Abraham who are not B'nei Yisrael. This doesn't seem to be a focus of the Noahide movement, and I presume there is a good reason for this---what is it?

Answer 1

As explained in The Meaning and Significance of Zera Avraham we can see the following:

The Gemarah itself expresses this distinction as well. In Meseches Sanhedrin (59b), the Gemarah derives that the mitzvah of bris milah applies only to the descendants of Yitzchak, but not to the descendants of Yishmael, from the possuk: "Va'ata es brisi tishmor, v'zar'acha acharecha l'dorosum - and as for you, you shall keep my covenant, you and your offspring after you throughout their generations" (Bereshis 17:9). The Gemarah reasons that bnei Yishmael could not possibly be included in this commandment, because the term "zera" refers specifically to the descendants of Yitzchak, as the Torah states, "Ki b'Yitzchak yikarei l'cha zerah - since through Yitzchak will offspring be considered yours" (Bereishis 221:12).

Also see Was Esau commanded in circumcision? In which one answer states that Eisav was not circumcised at eight days and absolutely refused to do so when he became older. There are others who say that while he may have been circumcised at eight days, he refused to circumcise his children and they were seperated so that only Yaakov continued the line.

This means that the descendants of Eisav dropped bris milah in the generation of Eisav's children.

The descendants of Yishmael still keep bris milah as a result of their conversion to Islam. However, there is no way of telling which groups among them are currently Bnai Avraham. We should also note that the children of Avraham and Keturah apparently never took on bris milah because it was restricted to zerah Avraham and only Yitzchak is called zerah Avraham. Yishmael had bris milah only because he was born before Yitzchak and he was part of the household of Avraham at that time.

While we might say that originally, the descendants of Eisav, Yishmael, and Keturah might have been subject to the requirement of bris milah (only from the original commandment in Lech L'cha) we cannot identify any of them nowadays. Since they would have been intermarried with all the nations around them, their identity has been totally lost. The connection of Eisav with the Romans is on a hashkafic level only as is the connection of the Arabs (or Muslims) and Yishmael.