Is it right for two thousand Muslim men from the village to seclude themselves and pray individually because they were late for the Eid prayer and differed on how to perform it?

The harmony among Muslims and the unity of their word are among the greatest objectives of Islamic law (Sharia (definition)). Allah Almighty says: ﴿And hold firmly to the rope of Allah all together and do not become divided.﴾ You must know that the methodology of the Salaf (pious predecessors) is not for division among Muslims. This harmony and unity become even more imperative if the division is due to jurisprudential branches where disagreement is permissible. The methodology of the Salaf is broad in this regard, and they permit praying behind an Imam who differs from the worshipper in some jurisprudential issues. There is no disagreement among Muslims regarding the time of Eid prayer, as all madhhabs (schools of thought) have agreed that the end time for both Eid prayers is the zenith of the sun (zawal). The majority of jurists said that the time for both Eid prayers begins when the sun has risen to the height of a spear and extends until the beginning of zawal, while the Shafi'is said its time is between sunrise and zawal. It is recommended to perform the Eid al-Adha prayer earlier to extend the time for sacrifice, and to delay Eid al-Fitr prayer to extend the time for giving out zakat (definition) al-fitr. The advice is to gather behind one Imam for both Eid prayers, Jumu'ah (Friday) prayer, and congregational prayers, and not to cause disunity among Muslims.