Gemara

(Mishnah - R. Meir): The day he (the king's father) died... (Chachamim forbid the day of death only if they burned his Kelim.)

Inference: R. Meir always forbids. He must say that burning is not a Nochri statute, and Chachamim say that it is a Nochri statute!

Question (Beraisa): We burn after a king dies. This is not forbidden due to 'ways of the Emori (doing like Nochrim)';

If it is a Nochri statute, this is "uv'Chukoseihem Lo Selechu"!

Answer: All agree that it is not a statute. It just shows honor to the king. R. Meir holds that they serve idolatry in any case. Chachamim hold that they serve idolatry only if they burned, for then the death is meaningful to them.

(Beraisa): We may burn after a king dies. This is not forbidden due to Darchei ha'Emori - "uv'Misrefos Avosecha ha'Melachim..."

Sanhedrin 52b (Beraisa - R. Yehudah): I agree that it is disgraceful (to rest the head on a block and cut it with a chopping knife), but we cannot execute by the sword like the kingdom - "uv'Chukoseihem Lo Selechu"!

Chachamim: Since the Torah teaches that a sword should be used, we did not learn from the Nochrim.

74a (Rava bar Rav Yitzchak): Wearing shoelaces like Yisraelim is a a light Mitzvah (which one may not transgress in public, even if he will be killed)..

Shabbos 67a (Mishnah - R. Meir): One may go out (on Shabbos) with a locust egg, the tooth of a fox, or a nail from a crucifix for the sake of a cure;

Chachamim forbid these at all times, due to Darchei ha'Emori

The locust egg is (hung in the ear) for an ear ache. A tooth from a live fox helps one who sleeps too much, and a tooth from a dead fox helps one to sleep. A nail from a crucifix helps for swelling (due to a blow from iron).

(Abaye and Rava): Anything done to heal is not Darchei ha'Emori. If it does not (have a logical or medical reason for it to) heal, it is Darchei ha'Emori.

(R. Chiya bar Avin): Everything in Perakim 7 and 8 of the Tosefta of Shabbos is Darchei ha'Emori, except for two cures. If a bone is caught in one's throat, we put a similar bone on his forehead and say 'Chad Chad Nachis Bala Bala Nachis Chad Chad.' If a fishbone is stuck, we say 'Ninatzta k'Machat...'

Rishonim

Rif and Rosh (Sanhedrin 17b and 8:3): Nochrim used to wear red shoelaces, and Yisraelim wore black, to avoid Bigdei Nochrim. If a Nochri tells a Yisrael 'wear red shoelaces in public, or be killed', he may not wear them.

Rambam (Hilchos Avodah Zarah 11:1): One may not follow Chukos ha'Nochrim or resemble them in their dress or hairstyle - "uv'Chukoseihem Lo Selechu." Yisrael should be distinguished from them in clothing and other deeds. One may not wear clothing special to them.

Rambam (15): All matters (of witchcraft and Nichush) are false. Early idolaters tricked people into following them. One who thinks that it is true, but the Torah forbids it, is a fool. "Ha'Goyim... El Me'onenim Yishme'u v'Atah Lo Ken..."

Rambam (Hilchos Yesodei ha'Torah 5:2): If a Nochri seeks to make a Yisrael transgress an Aveirah other than idolatry, Arayos or murder, if 10 Yisraelim are present, in which case he must submit to be killed.

Rashi (74b DH Arkesa): If Yisrael tie their shoelaces differently, for they are more modest, even if it is not a Mitzvah, rather, a custom, he must be Mekadesh Hash-m in front of his colleagues.

Rashba (1:413): The Rambam says that what the Torah forbade is folly. I disagree. Sanhedrin 101a permits asking Shedim via oil or egg shells, because they lie. Sha'ul used an Ov (to speak to Shmuel). The Torah testified that the Mitzriyim did things through Kishuf. A Rav derived from the Rambam that whatever works is permitted. He used this to permit a nail from a crucifix. This is unlike a fox' tooth, which works due to itself, like a magnet. The crucifix nail works not due to the iron or its shape, rather, from what is received from the crucifix. On Shabbos, one may go out with a special stone to prevent miscarriage, or something that weighed the same as such a stone (Shabbos 66b). The Mishnah permits a nail from a crucifix and a fox' tooth, for they were believed to heal. We may rely on what was once known to heal, or what we see nowadays that it heals. We may rely even on simple people, who are not Chachamim or doctors. However, in Moreh Nevuchim the Rambam forbids what we cannot explain why it should work, due to Darchei ha'Emori. We may rely on what Chachamim permitted. However, they permitted thngs that we cannot explain! R. Chiya bar Avin forbids almost everything, but even he permits, if one is choking on a bone, to put a similar bone on his forehead and say 'Chad Chad...' There is no logic for this action or these words. Presumably, he permits because experience shows that it works. The Gemara is full of such matters. It is very concerned for Zugos (even numbers of things), and asked why Chachamim enacted four cups of wine!

Tosfos (Sanhedrin 52b DH Ela): Here we permit a Nochri statute because it is written in the Torah. In Avodah Zarah, we say that burning after a king dies would be forbidden if it were a Nochri statute, even though there is a verse for it! There, we mean that it is not an idolatrous rite. If it were, it would be forbidden in spite of the verse. Here we discuss a Nochri rite not for idolatry.

Ran (2b DH Sorfin): The Torah forbids (due to Darchei ha'Emori) only folly. All of it is for the sake of idolatry. What is done for a reason is permitted. We burn after a king dies for honor, to show that others may not use what he used.

Radvaz (2:740): People slaughter chickens on Erev Yom Kipur for Kaparah. I did not see any Chacham protest. The Rashba forbids. I say that if they give the chickens to the poor, it is not Darchei ha'Emori, and even he would permit. One may give Tzedakah 'in order that my son will live'!

Poskim

Shulchan Aruch (YD 178:1): One may not follow Chukos ha'Nochrim (Rema - or resemble them), or wear dress special for them, or grow his hair the way they do...

Gra (1): Toras Kohanim forbids their Nimusim, e.g. theaters, and circuses. R. Meir says that this is Darchei ha'Emori.

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 something they made a custom and statute without reason. Then we are concerned for Darchei ha'Emori and affairs of idolatry.

Shach (3): It is more modest to wear black. This helps one who was seized by his Yetzer ha'Ra. Our tradition is not to wear red.

Gra (6): The Rif could agree with Rashi. What is done for honor is permitted, even if Nochrim originated it.

Rema (ibid.): If there is a reason for it, e.g. doctors wear special clothing, it is permitted. The same applies to clothing for honor or other reasons. This is why one may burn after the death of kings.

Beis Yosef (DH v'Chen): Maharik (88) says that in two cases we forbid due to Chukos ha'Nochrim. One is if there is no revealed reason for it, like 'Chok' connotes. Since he does a strange matter without a reason, it looks like he is drawn after Nochrim and admits to them (their creed). Semag (Lavin 50) says that in Shabbos, Chachamim listed all traditions they had for Nochri practices. Every one in the Tosefta (Perakim 7,8) is bizarre; we do not know any reasons for them, like those listed in Shabbos 67a. Chukoseihem are what is astounding. Darchei ha'Emori are Nichushim. We also forbid due to Chukos ha'Nochrim a breach of modesty and humility that Nochrim do, if the Halachah follows the Tana (Sifri Re'eh 29) 'since they go out in purple, I will also. Since they go out amidst praises, I will also.' These are haughtiness. This is if he seeks to be like them, without any other purpose. If the Yisrael manner of dress is no more modest, Rashi permits dressing like the Nochrim. The Rambam says that Yisrael must be distinguished from Nochrim. Maharik does not always require this. He forbids a garment special for Nochrim, but not what resembles their garments! Rather, we forbid only what is special to them, and Yisrael refrained from it due to modesty or another reason. In this case, one who wears it looks like he admits to them and is drawn after them.

Gra (7): The Ran says that Darchei ha'Emori forbids only folly. It is all for the sake of idolatry. What is done for a reason is permitted. Sanhedrin 52b connotes oppositely! There is reason to execute like the kingdom, to minimize disgrace, yet Chachamim would forbid due to Darchei ha'Emori had the Torah not specified a sword! Tosfos explains that a verse permits a Nochri rite unless it is for idolatry. In Avodah Zarah we answered that burning after a king dies is for honor, and not for idolatry. Maharik must explain that there is no reason to kill by the sword. This is difficult! Rather, if not for the verse, we would not kill by the sword at all. It is still difficult, for the Torah did not specify to cut off the head! The Ran and Rema are very difficult. Rather, even if their rite came first, it is permitted if we did not learn from them, even without a verse, as long as we would do so even without them. The Rif connotes like this. Surely a shoelace is not immodest. This is why it says even a shoelace. The Maharik's proofs are invalid, for those clothes were not special only for Nochrim.

Avnei Nezer (YD 128:4, 131:5): The Rambam explains that one must be Moser Nefesh even for shoelaces, due to 'uv'Chukoseihem Lo Selechu. The Maharik says that this Aveirah is only when one wants to mimic Nochrim! We must say that even though he does so only due to the coercion, the Nochri will not think so. Even though the Yisrael does not transgress, due to his intent, Kidush Hash-m applies.