Ruling on Moon Sighting for `Eid
Question

Regarding starting fast and breaking fast times in Ramadan month, I don't observe a certain crescent, but I start my fasting of the holy month based on testimony of two straight Muslims. The problem is that the people of my country always start fast one day later and breaking fast one day earlier than all Muslim majority all over the world. I am much of the opinion that we should all be unified in fast times, so I fast and break fast with the majority. We are all Muslims in Islam countries from Indonesia to Morocco. My question is about the Eid prayer, I can't travel to pray Eid, if I pray it with my country (knowing that this way it will be later), is it acceptable? Or should I not pray with them (then I miss the reward and blessings of it)? Finally, I find nothing to say but "All power of change is really Allah's".
Praise be to Allah.Importance of unity in Islamic observances
If the people of your country rely on moon sighting as prescribed in Shari`ah, then you should start and end the fast with them, and you should not differ from them and follow the moon sighting of another country . 
The Prophet (blessings and peace of Allah be upon him) said: “The fast is the day when you fast and Al-Fitr is the day when you break the fast, and Al-Adha is the day when you offer the sacrifice.” (Narrated by At-Tirmidhi, 697, who said: some of the scholars interpreted this Hadith as meaning that the beginning and end of the fast should be observed with the main body of Muslims and the majority of the people.) The Hadith was classed as authentic by Al-Albani in Sahih At-Tirmidhi. 
Moon Sighting: Local vs. Global Perspectives
If you follow the Madhhab of those who think that sighting the moon in one country is binding upon all countries, and this means that `Eid for you comes before their `Eid, then you should conceal the fact that you have broken the fast and offer the `Eid prayer with them on the following day. 
The importance of avoiding public disputes over moon sighting
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
… If you think that the first opinion should be followed and that if the sighting of the new moon is proven in any part of the Muslim world in the manner prescribed in Shari`ah and that it is binding to act upon that, but your country does not follow that and follows one of the two other opinions, then you should not openly show that you are differing from them, because of the trial and confusion and arguments that may result from that. You can fast secretly at the beginning of Ramadan and break the fast secretly at the beginning of Shawwal. As for differing openly, that is not appropriate and it is not something that is enjoined by Islam. (End quote from Majmu` Fatawa Ash-Shaykh Ibn `Uthaymin, 19/44)
For more details, please see the following answers: 1226 , 1584 , 207382 , 66219 .
And Allah knows best.