Gemara

(Mishnah): The Megilah is read on the 11th, 12th, 13th, 14th, and 15th.

Question (Reish Lakish): This transgresses "Lo Sisgodedu" - do not have differing factions!

Question: "Lo Sisgodedu" forbids wounding oneself in grief over a Mes!

Answer: "Lo Segodedu" would have taught that. The Torah wrote "Lo Sisgodedu" to forbid also factions. Had it come only for factions, it would have said 'Lo Sagodu'.

Counter-question: (R. Yochanan): Why didn't you ask from a prior Mishnah?

(Mishnah): Where the custom is do work on Erev Pesach, we work until noon. Where the custom is not to work, we do not work.

Answer #1 (Reish Lakish): I asked regarding an Isur. Why do you suggest I should ask regarding a custom?

(Rav Shemen bar Aba): "To fulfill... in their times" - Chachamim enacted many times (to read Megilas Esther).

Question: Also working on Erev Pesach is an Isur!

(Mishnah): Beis Shamai forbid working the previous night;

Beis Hillel permit.

Answer (Reish Lakish): There, if one does not work he looks like one who has no work to do (so it is not a problem of factions).

Question: In our Mishnah, Beis Shamai permit the Tzaros to the brothers and Beis Hillel forbid them!

Answer (Reish Lakish (and Rav)): Beis Shamai did not follow their own teachings.

Question: R. Yochanan and Shmuel say that Beis Shamai followed their own teachings. According to them, this transgresses "Lo Sisgodedu"!

Answer #1 (Abaye): The Isur applies only to two Batei Din in one city, one of which rules like Beis Shamai and one like Beis Hillel. Batei Din in different cities may rule differently.

Objection (Rava): Beis Shamai and Beis Hillel are like opposing Batei Din in the same city!

Answer #2 (Rava): The Isur is when half the judges on a Beis Din in a city rule like Beis Shamai, and half rule like Beis Hillel. We may have two opposing Batei Din in one city.

Question (Beraisa): In R. Eliezer's region, they would cut trees on Shabbos to make coals to forge a knife for circumcision (but not in R. Akiva's region).

(Beraisa - R. Akiva): Any Melachah that can be done before Shabbos is not permitted on Shabbos (for the sake of Milah).

Answer: We said that different regions may conduct differently!

The one who asked the question thought that because Shabbos is so stringent, it is like one place (all places must conduct the same way).

Rishonim

Rif and Rosh (1:9): The Gemara asks why the argument about Tzaras Ervah and the different days for reading the Megilah does not transgress Lo Sisgodedu. Rava concludes that the Isur is only when half the judges on a Beis Din in a city rule like Beis Shamai, and half rule like Beis Hillel. We may have two opposing Batei Din in one city, all the more so in different cities.

Shiltei ha'Giborim (3b:1): Also nowadays that there are arguments between Chachamim and Ge'onim, the city may not be divided. They must vote and follow the majority.

Question: Why may villagers read early in cities that read later? This is like a divided Beis Din in one city!

Answer #1 (Rosh): It is not Lo Sisgodedu because the difference is not due to an argument, rather, to residence. If a Ben Ir went to a village, he would read like them. This is not like two Toros. This is why R. Yochanan did not answer Reish Lakish. Rather, he said that he should have asked from elsewhere.

Answer #2 (Rosh): Reading the Megilah on different days is like two Batei Din in one city. Villagers used to read for themselves in the cities. The Yerushalmi says that a Ben Ir cannot be Motzi a villager.

Answer #3 (Tosfos 14a DH Ki): Villagers gathered to read early in their own village.

Rambam (Hilchos Avodah Zarah 12:14): The Isur Lo Sisgodedu includes not having two Batei Din in one city, this acts one way and this acts differently. This causes great arguments. The Torah forbids having many factions.

Question #1 (Kesef Mishneh): Why does the Rambam rule like Abaye against Rava?

Answer #1 (Kesef Mishneh): The rule that the Halachah follows Rava against Abaye does not apply when they argue about what others said.

Objection (Lechem Mishneh) Abaye's opinion was rejected!

Answer #2 (Teshuvas Radach Beis 13, cited in Kesef Mishneh): The Rambam means that when there are different customs in a city, this makes it (like) opposing Batei Din. Perhaps the correct text of the Rambam should say 'we cannot have like two Batei Din in one city.

Lechem Mishneh: Perhaps the Rambam rules like Rav, who says that Beis Shamai did not follow their own teachings, for we follow Rav against Shmuel in Isurim. Shmuel permits two opposing Batei Din in one city (e.g. Beis Shamai and Beis Hillel). He forbids only when one Beis Din is divided. Rav forbids two Batei Din only in the same city. All agree that different places read the Megilah on different days. The Rambam holds like Tosfos, who says that villagers read early in their own village. However, the Gemara concludes that Beis Shamai followed their own teachings!

Question: The Rambam (12:13) obligates lashes for one who scrapes himself (out of grief) over a Mes. He should exempt, for this is Lav shebi'Chlalos (different Isurim forbidden by one Lav), like "Lo Sochlu Al ha'Dam"!

Answer (Kesef Mishneh): The primary Lav is scraping oneself. We also include having factions. Regarding "Lo Sochlu Al ha'Dam", we do not know which is the primary Isur.

Poskim

Rema (OC 493:3): In many places the custom is to shave (during the Omer) until Rosh Chodesh Iyar. They should not shave after LaG b'Omer, even though they may shave on LaG b'Omer itself. The places that shave from LaG b'Omer and onwards may not shave at all from Pesach until LaG b'Omer. One city should not conduct partially like this custom and partially like another, due to Lo Sisgodedu. All the more so one may not be lenient like both.

Magen Avraham (6): We learn from the Gemara that Lo Sisgodedu does not apply to customs, only to Isurim. It is not a problem if people will think that he does not intend for Isur, e.g. he does not work because he has no work to do. The same applies to shaving; people will say that others do not want to shave.

Question (Korban Nesan'el 4, Me'il Tzedakah (99) and R. Akiva Eiger): If Levi sees David shaving when Levi holds that it is forbidden, this is Lo Sisgodedu!

Magen Avraham (6): However, we conclude that the Isur applies to a divided Beis Din in one city. It is possible that it applies in every such case. Tosfos (Pesachim 14a DH Shtei) brings from the Yerushalmi that it is proper to be stringent (about working on Erev Pesach) in Yerushalayim because people gather there and some are from places where they are stringent. I.e., to have differing practices would transgress Lo Sisgodedu. It seems that the Rif and Rosh explain this way, for they bring only Rava's conclusion (without distinguishing between custom and Isur, or when it does not look like one holds that it is forbidden).

Rebuttal (Korban Nesan'el 4): These distinctions apply also in the conclusion. This is why we could not prove that Beis Shamai followed their own teachings from the cases of enlarging the Sukah and the opening to the Mikveh, for it was not evident that these were done for Halachic reasons!

Eshel Avraham (6): The Yerushalmi is stringent mid'Rabanan, to avoid strife. Lo Sisgodedu is mid'Oraisa. It applies only to chronic differences of conduct, but not to one who went to a place that conducts differently.

Magen Avraham (6): The Tur's Kitzur Piskei ha'Rosh (1:9) says that we are not concerned if people from different places gather and each follows its practice. This is like the Rosh's first answer (above). I say that this is only when each agrees that the other acts properly, e.g. Megilah, or places that have a custom to say Selichos on certain days. If there is an argument about whether or not something is Asur, e.g. Chelev stuck to the stomach under the membrane (Benei Rinus permit it, but other places forbid it), if people of different practices gather together they must adopt a uniform law to avoid Lo Sisgodedu.

Magen Avraham (6, DH uv'Keneses): Poskim disagree about whether or not Lo Sisgodedu applies when some people adopted a Cherem. Lo Sisgodedu does not apply to one who keeps the stringencies of the place he left, or if people of one profession conduct differently than everyone else. One may follow different stringencies if he is unsure of the Halachah, like R. Akiva who took two tithes from an Esrog.

Alshich (Teshuvah 59): In Blarta they made fences and Isurim for an Arus to enter his Arusah's house. They wanted to impose it on the congregation in Polaisi, which did not accept it. R. David Vital said that Lo Sisgodedu does not apply, for the Halachah follows Rava who permits opposing Batei Din in one city. I say that Lo Sisgodedu does not apply at all here, only when the Isur has a source in the Torah or mid'Rabanan, for then it looks like two Toros.

Kaf ha'Chayim (468:65): Because the Halachah follows Rava, each congregation is like a city. One cannot force another to conform to its practices. Ashkenazim in Yerushalayim have their own Beis Din, so they should keep their practices. We do not follow the majority of the city, even for an Isur mid'Oraisa.