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There is a prohibition of creating factions among Jews when some Jews practice one law and others follow a different law.
Background and reason
- Some say that the reason for this prohibition is that when some Jews follow one law and other another, it gives the appearance as though there were two Torah's. Others, however, explain that the reason behind this prohibition is not to cause dispute between Jews. 
- Many poskim hold that there is a prohibition of Lo Titgodedu regarding a difference of minhagim.
- Some say that there is no prohibition of Lo Titgodedu when it comes to praying according to one's family minhag of davening in a shul which is davening according to a different minhag. There are poskim who only allow it for the private quiet parts of davening such as the silent Shemona Esrei.
- There is a long discussion of whether it is Lo Titgodedu for some people in one minyan to wear Tefillin on Chol HaMoed and others not to. See Wearing Tefillin on Chol HaMoed.
- Regarding the practice of standing during Kriyat HaTorah, see Shulchan Aruch 146:4 and Sh"t Betzel Chachma 5:1.
Two Established Minhagim
- If there are two established practices about what the halacha is, according to most poskim, there is no lo titgodedu to follow one's personal practice since it is a known dispute.
- For example, many permit following one's practice about wearing Tefillin on Chol Hamoed even if the congregation has a practice otherwise since it is an established dispute.
- For example, many permit reciting one's private nusach of davening since there are multiple established practices of davening.
- Gemara Yevamot 13b derives this prohibition of not making factions in Israel from the Pasuk of Lo Titgodedu (Devarim 25).
- Rashi (Yevamot 13b)
- Rambam (Avoda Zara 12:14)
- In the Gemara Yevamot 13b, Reish Lakish is recorded as saying that there is no prohibition of Lo Titgodedu regarding minhagim, Rabbi Yochanan however seems to disagree. See the Magen Avraham 493:6 who discusses as to what the conclusion of the gemara was. The Chazon Ovadia Sukkot p. 353 leaves it as a safek and is strict. See also Rambam (Avoda Zara 12:14) who implies this. See Rabbi Zilberstien's sefer on Parshat Reeh who suggests that this question depends on the underlying reason of Lo Titgodedu discussed above. Rabbenu Yerucham Netiv 2 quoting the Ramah writes that there's no issue of lo titgodedu regarding minhagim. Rama O.C. 493:3 and Magen Avraham 493:6 hold that there is lo titgodedu for minhagim. Radvaz 3:523, Chatom Sofer 6:86, and Peot Hashulchan 3:14 fnt. 22 agree. See Yabia Omer O.C. 6:10:6. Chesed Lalafim O.C. 1:9 holds that there's no lo titgodedu for minhagim. He proves it from Ran end of Rosh Hashana regarding blowing all types of truot.
- Yalkut Yosef (Tefillah v. 1 pp. 399-403), Yabia Omer O.C. 6:10 (see also Yabia Omer E.H. 6:14:6 regarding the logic he presents about how the disputes between Ashkenazim and Sephardim are long standing and do not pose a question of Lo Titgodedu like two bet din's in one city).
- Igrot Moshe O.C. 2:23, Heishiv Moshe 1:17
- In Gemara Yevamot 14a Rava and Abaye argue about why we could have some people read megillah on one day and some on another day and it isn't an issue of lo titgodedu. Abaye says that as long as there's two established practices in two towns there's no issue of lo titgodedu. Rava limits it further and says that even if there's two established practices in one town that would also avoid the issue of lo titgodedu. Although the Rambam Avoda Zara 12:14 follows the opinion of Abaye, the majority of rishonim hold otherwise (Rabbenu Yerucham Netiv 2 cited by Bet Yosef YD 242:4, Bet Yosef 624:5, Tashbetz 3:179).
- Yabia Omer O.C. 6:10:6 quotes the Parshat Mordechai O.C. 4 who writes that it is permitted for some people in shul to wear Tefillin and others not to since it is a known established dispute and doesn't incur lo titgodedu. Igrot Moshe O.C. 4:34 forbids having some people in shul wearing Tefillin and some not wearing Tefillin.
- Yabia Omer 6:10