There's always a debate as to when the moon was sighted and people don't always agree on the same dates. What can you do if your family and friends begin or end Ramadan on a day differently than you?
The Islamic calendar is based on the lunar calendar, and so the start and end dates for Ramadan and Eid differ every year... But we have to maintain a sense of unity.
Shaykh Yasir Qadhi discusses and answers the question
My dear brothers and sisters in Islam, our Prophet (sallallahu alaihi wa salam) encouraged unity of the Muslims, and he said ‘Allah's hand is over the jama’aa, over the group.’ And especially when it comes to Ramadan, our Prophet (sallallahu alaihi wa salam) said that Ramadan is the day when you all begin to fast and the Eid Ul Fitr is the day when you all stop to fast. So more important than the methodology that you use- whether it is moon sighting, whether it is global, whether it is this, whether it is that. The unity of the community is more important than any of these principles of fiqh.
So if you are living in a land of Islam and the government, or their Mufti, or the official administration announces that the whole country should fast on this day and stop its fast on this day, then you will follow the people of the land. Because Allah's mercy comes with unity. And if you're living in lands that are not governed by Islam, and so every community is following itself, then you follow the majority and you follow your locality and your Masjid. You follow the people that you associate with and try your best to achieve some type of majority within, at least your city, or at least your community.
So the point is that you yourself should not break away from your family and friends. Try your best to stick together and celebrate Ramadan as a whole, and realize that these are not issues where we should be divided over. Even if one Masjid begins on one day and the other Masjid begins on another, this is a difference in fiqh that is permissible. And Allah (azza wa jal) will not punish either of these two groups, even if unity could not be achieved. So stick with the jama’aa, stick with the group of people, stick with your family and friends, and try to form a unified position amongst yourselves. That is what is going to be best in this scenario.