Gemara

Once, the Romans decreed that the Yisraelim may not observe Shabbos, circumcision and Nidah. R. Reuven ben Istrobli cut his hair Kumi (like a Nochri), and sat with the legislators.

R. Reuven: Does one want his enemy to become poor, or to become rich?

The legislators: He should become poor!

R. Reuven: If so, we should allow the Yisraelim to cease from working on Shabbos, in order that they will become poor!

The legislators: You are right. (They repealed the decree.)

Sotah 49b (Beraisa): Chachamim cursed anyone who will teach his son Chachmas Yevanis.

Question: Half of the children of R. Gamliel's house learned Chachmas Yevanis!

Answer: It was permitted to R. Gamliel's house, for they were close to the king;

(Beraisa): One who cuts his hair Kumi transgresses 'Darchei (going in the ways of) ha'Emori (Nochrim)';

This was permitted to Avtulus ben Reuven, for he was close to the king.

They permitted R. Gamliel's house to learn Chachmas Yevanis, for they were people close to the king.

Rishonim

Rambam (Hilchos Avodah Zarah 11:3): If a Yisrael is close to the kingdom and needs to sit in front of their kings and it would be disgraceful if he did not resemble them, he may wear their clothing and shave opposite his face the way they do.

Kesef Mishneh: They permitted Avtulus to cut his hair Kumi, for he was close to the king. The Rambam learns that all the more so, this reason permits clothes of Nochrim. Also, Avtulus pretended to be a Nochri, and through this he was able to save Yisrael. Surely he dressed like a Nochri. If he dressed like a Yisrael, they would have realized that he is a Yisrael!

Teshuvas ha'Rambam (244): Mi'Divrei Sofrim, one may not cut the hair only on the front of the head, or only on the back, or cutting around and leaving the hair in the middle, for this is (the custom of) Nochrim, and the Torah said "v'Lo Selchu b'Chukos ha'Goy(im)." Cutting in the place of Tefilin is called "Kumi." This was permitted only for people close to the king, in order to protect Yisre'elim, like it says in Sotah.

Tosfos (Bava Kama 83a DH Hitiru): From the beginning, Chachamim did not decree about people close to the king. Avtulmus was close to the king, like we find in Me'ilah.

Kovetz Shi'urim (1 Bava Kama 98): Tosfos connotes that the Isur is only mid'Rabanan. This is difficult. Darchei ha'Emori is an Isur Torah! The Rambam says that one is lashed for it. The Kesef Mishneh says that since Chachamim were authorized to decide what is Darchei ha'Emori, they could permit for people close to the king. This is difficult. They were authorized to define the Isur, but not to permit what is Asur! Maharik (192) derived from the Beraisa 'one should not say 'since they go in purple...'' It did not simply say 'one may not go like they go.' This shows that the Isur is only if one desires to be like them. We permit dressing like them for a benefit or honor, or those close to the king who do so for the sake of the Rabim. However, why does it say 'they permitted'? There was no need for a Heter! Perhaps it means that they needed to publicize why it is permitted, to avoid Chilul Hash-m that important people cut their hair Kumi.

Question (Minchas Chinuch Mitzvah 262:2): In Sanhedrin (52b), we find that R. Yehudah forbids Misas Sayif through the sword because it is a Nochri ritual, even though there is a reason (it is more dignified). Chachamim disagree only because it is written in the Torah!

Bartenura (Kil'ayim 9:2): The Mishnah forbids wearing Kil'ayim even in order to evade a tax collector who steals. My Rebbeyim explain that he collects only from Yisre'elim, and one wants to wear Kil'ayim in order to look like a Nochri.

Bartenura (Miketz 41:14): For Kevod Malchus, Yosef was permitted to shave (his beard and sideburns).

Chasam Sofer (Miketz 41:14): Rashi explains that Yosef was permitted to shave due to Kevod Malchus. I.e. it was Rosh Hashanah. Kevod Malchus, even for a Nochri king, overrode Yom Tov.

Note: Surely, the Chasam Sofer understands that he shaved the head, but not beard and sideburns, like 'Elu Megalchim' (Mo'ed Katan 13b. It lists people who may shave during Chol ha'Mo'ed.)

Poskim

Shulchan Aruch (YD 178:1): One may not go in the ways of the Nochrim (Rema - or resemble them). One may not wear clothing special for them, or grow his hair the way they do...

Rema: One must differ from them in dress and actions. This refers to a Nochri custom for the sake of immodesty, e.g. to wear red clothing, which nobles wear, or a custom and statute without reason. If there is a reason for it, e.g. doctors wear special clothing, or clothing for honor or other reasons, it is permitted.

Shulchan Aruch (2): If one is close to the kingdom and needs to wear Bigdei Nochrim and resemble them, all is permitted.

Beis Yosef (DH Mi): They permitted R. Gamliel's house to learn Chachmas Yevanis because he was close to the king. The Rambam says that one is lashed for all of these. If so, how could Chachamim permit it for those close to the king? Perhaps they permitted it because when Yisre'elim are close to the king, they can annul decrees, like in Me'ilah and Ta'anis (22a). David had 400 children who cut their hair Kumi and grew Bluris, and they were at the front of the troops to frighten the enemies. Alternatively, the Torah did not detail anything (what is Darchei ha'Emori). Chachamim were authorized to decide what is forbidden, and they chose not to decree about those close to the king.

Bach (7): I say that this is not a question. "Uv'Chukoseihem Lo Selechu" connotes one who desires to resemble them and act like them. It seems that he admits to their creed. The Sifri says 'since they go in purple, I will also...' If one does not desire to be like them, but he must dress like them to avoid disgrace, the Torah never forbade this. The Rambam connotes like this. Surely, there was a tradition that this is the meaning of "uv'Chukoseihem..."

Taz (5): Even though everything in this Siman is mid'Oraisa, and Chachamim do not have the power to uproot a Torah Isur, here is different, for the Torah did not specify and authorized Chachamim to decide what is forbidden.

Teshuvah me'Ahavah (in Yalkut Meforshim in Friedman Shulchan Aruch): This is like the Beis Yosef's latter answer. According to the first answer, one may be lenient even for other Isurim. Tosfos holds like the latter answer.

Beis Yosef (DH Kasvu): Hagahos Maimoniyos (Avodah Zarah 11:1, citing Re'em) says that we cannot add based on our reasoning to what Chachamim forbade due to Darchei ha'Emori. They had a tradition what is Darchei ha'Emori. Semag says that all of it is in the Tosefta in Shabbos (7:1). Many people do not pay attention, and transgress. Perhaps they think that only what is in the Gemara is forbidden, and we do not follow the Tosefta regarding everything else. If not, the Gemara would not have omitted everything else!

Chadrei De'ah (in Yalkut Meforshim): The Bartenura in Kil'ayim seems to support the Bach. The Mishnah connotes that we forbid only due to Kil'ayim, but not for pretending to look like Nochrim. We must say that since he seeks only to exempt himself from Ones, it is permitted. However, the Rosh explains that they do not collect from the clothes one wears. If so, he could hold that one may not dress like a Nochri in such a case, even without the Isur Kil'ayim.

Hagahah (ibid.): Perhaps he refers to the Rosh's Hilchos Kil'ayim 9:9, or the text should say 'R. Shimshon.'

Erech Lechem: We do not permit (Darchei ha'Emori) for the sake of evading taxes.

Chadrei De'ah (ibid.): I proved (182:2) that it is permitted mid'Oraisa and forbidden mid'Rabanan. It is permitted (even mid'Rabanan) only for Shalom Malchus. Really, the Bartenura supports the Beis Yosef. Here we cannot be lenient for the sake of a need. That Heter is only for a Mitzvah, but not when he dresses like them in order to resemble them and be close to them. This is the Torah Isur! Rather, the Torah empowered Chachamim to be lenient to permit where they see a need. The Beis Yosef (YD 178 DH u'Mah she'Chosav v'Chol) struggled to explain why Perush ha'Mishnayos (Avodah Zarah 1:3) exempts from lashes. He said that it is Lav shebi'Chlalos (different Isurim forbidden by one Lav). This is wrong. Rather, since the Torah empowered Chachamim, it is not a proper Lav to be lashed.

Tur (181): The Rambam says that the Isur of cutting the sideburns is because the Nochrim do so. Chazal did not explicitly say so. We need not give reasons for Mitzvos.

Taz (181:1): Since the Rambam says that it is an Isur of Nochri rites, sometimes it is permitted, e.g. for Shalom Malchus, like we find in 178:2. Shalom Malchus permits only Isurim due to Nochri rites.

Minchas Chinuch (251:1): Mishnas Chachamim (53, Yavin Shemu'ah 2) asked that the Beis Yosef's answer (Chachamim could permit for people close to the king because the Torah did not explicitly teach which are forbidden, we cannot say so about cutting the Pe'os, which is explicit! The Taz is difficult. Surely, in each generation the Isur is based on what Nochrim do then. Even if they will not cut the Pe'os, surely it is forbidden to us! Regarding Chukos ha'Nochrim, the Rambam said 'like the Nochrim do. Regarding Pe'os, the Rambam said 'like the Nochrim used to do.' I.e. it does not depend on what they do now.

Divrei Chayim (1 YD 30): The Isur to go in the ways of the Nochrim is not to lower their honor. We need not evade their company. We find that great Chachamim and Chasidim were constantly in the house of the king and his officers, e.g. R. Avahu, R. Yehoshua, Shmuel and Rava. Rather, the Torah gives many fences to guard from haughtiness and Arayos. We should not go in the ways of the Nochrim, who were not commanded to make fences for their seven Mitzvos. The Torah was given to Yisrael because they are brazen (Beitzah 25b). I.e. they are prone to haughtiness, Arayos, theft, etc. due to their Midos, therefore they need extra fences. The Nochrim refrain from these due to their nature. Maharik (192) says that we must guard not to go in their ways when there is concern for lewdness, adultery or obscenity. If one does not intend to be like the Nochrim, it is permitted. He refers to one who one who intends for a benefit, e.g. a doctor who wears a doctor's uniform for monetary purposes, but not in order to dress obscenely or to adorn oneself in front of people. However, the Rema permits only when Nochrim do the rite for a monetary or other benefit. If they do so for lewdness, it is forbidden to Yisrael, even if he does so for a benefit! Tosfos, the Bach, Maharik and the Beis Yosef permit when the Yisrael does not intend to resemble them. It seems that Kiryat Sefer disagrees. He says that Chachamim had a tradition for what are their rites. If it depended on intent to resemble them, we would not need a tradition! Even if one wears other garments that show that he is a Yisrael, if he wears one immodest garment of Nochrim, he transgresses. The Tosefta transgresses wearing purple (in every case), even if his other garments are of Yisrael.