OPINIONS: The Mishnah states that when one makes a Neder to prohibit benefiting from Arelim (uncircumcised people), he is permitted to derive benefit from an Arel who is Jewish, and he is prohibited to derive pleasure from any Nochri, even one who is circumcised. Since the intent of one's Neder is determined by the way most people speak, and the word "Arelim" is used colloquially to refer to all Nochrim (regardless of whether or not they are circumcised) and not to Jews, it is clear that the person who makes such a Neder wants to prohibit himself from deriving benefit only from Nochrim.
What, however, is the Halachic status of a Jew who intentionally refuses to have a Milah? Does the Mishnah mean that all Jews are automatically considered circumcised even if they intentionally refuse to have a Milah, or does the Mishnah refer only to Jews who want to have a Milah but are unable to for reasons beyond their control (such as reasons of health)?
(a) The RAMBAM (Hilchos Nedarim 9:21), CHIDUSHEI HA'RAN, and ME'IRI (in the name of TOSFOS; see also TOSFOS to Avodah Zarah 27a, DH Ika) maintain that even a Jew who intentionally refuses to be circumcised is also not deemed an Arel. They seem to derive this from the words of the Mishnah here that says that the term "Arel" refers only to a Nochri.
(b) The RITVA maintains that only one who cannot be circumcised for reasons beyond his control (for example, his brothers died from Milah) is not considered an Arel. If, however, a Jew intentionally refuses to have a Milah, he is considered an Arel. The NIMUKEI YOSEF and ME'IRI explain that the term "Arel" refers to anyone who takes no interest in the Mitzvah of Milah and does not support it, and thus anyone who intentionally does not have a Milah is deemed an Arel.
The MISHNEH L'MELECH (Hilchos Nedarim 10:7) points out that the wording of the MEFARESH here implies that one who intentionally avoids having himself circumcised is not considered an Arel, but he is not considered a "Mahul" (circumcised person) either.
HALACHAH: The SHULCHAN ARUCH (YD 217:41) states that one who makes a Neder not to benefit from "Arelim" is permitted to benefit from a Jew who is uncircumcised. The Shulchan Aruch also rules (217:42) that one who makes a Neder not to benefit from "Mulim" is prohibited from benefiting from Jews who are uncircumcised. This ruling seems to be in accordance with the view of the Rambam who does not differentiate between intentional or non-intentional Arelim.
REBBI AKIVA EIGER (on the Shulchan Aruch) cites the BEIS YOSEF who writes that a Jew who intentionally avoids having himself circumcised is considered an Arel. According to the PRI CHADASH, however, one is considered an Arel only if he refuses to have a Milah out of a malicious desire to "anger" Hash-m.
The RASHASH in Avodah Zarah (27a) remains with a question as to why the Shulchan Aruch in Hilchos Nedarim implies that all Jews are considered to be Mulim, a clear contradiction to what he writes in the Beis Yosef as cited by Rebbi Akiva Eiger. Moreover, in Hilchos Milah the Shulchan Aruch writes that only a Jew who is an Arel against his will is considered a Mahul (and therefore is permitted to serve as a Mohel, as implied by the Gemara in Avodah Zarah). This ruling of the Shulchan Aruch seems to contradict his words in Hilchos Nedarim where he implies that no uncircumcised Jew is considered a Mahul.