It comes down to different methods of sighting. Sayyid Sistani says that the moon has to be sighted with the naked eye; Sayyid Khamenei rules that using a telescope is permissible. Astronomists also say that technically the new moon starts before it can be seen by either of these, but generally the ruling is that it has to be sighted.
Another issue is the 'sharing of the same night'. This method used to be used. I.e. if a region shares a night, then the declaring of the moon from one part of that region would apply to all. This is now no longer being used as a criterion. Instead, Sayyid Sistani and Sayyid Khamenei say that you must follow your local horizon, so usually the moon can be seen in Southern Europe before it can in Northern Europe; hence, Spain will have Eid one day earlier than England.
as salam alaikum
the are different opinions on how a person should see the new moon. The major ones can be summarized as follows:
SIGHTING THE NEW MOON LOCALLY (VALID FOR ALL PLACES THAT SHARE THE SAME HORIZON) WITH NAKED EYE
This is the fatwa of Ayatollah Khomeyni, Ayatollah Sistani, Ayatollah Mararem Shirazi, Ayatollah Shobeyri Zanjani, Ayatollah Subhani, Ayatollah Qorban Ali Kabuli and Ayatollah Muhammad Sadiq Sadr.
SIGHTING THE NEW MOON IN A CITY WITH NAKED EYE AND VALIDATING THE SIGHTING FOR ALL THE OTHER PLACES THAT SHARE WITH IT THE SAME NIGHT
This is the fatwa of Ayatollah Khu'i, Ayatollah Muhammad Baqir Sadr, Ayatollah Muhammad Araki, Ayatollah Ruhani, Ayatollah Ishaq Fayyad, Ayatollah Wahid Khorasani and Ayatollah Bashir Najafi.
SIGHTING THE NEW MOON LOCALLY (VALID FOR ALL PLACES THAT SHARE THE SAME HORIZON) WITH THE HELP OF A TELESCOPE
This is the fatwa of Ayatollah Khamene'i, Ayatollah Muhammad Taqi Bahjat, Ayatollah Fazel Lankarani and Ayatollah Muhammad Taqi Mudarrisi.
SIGHTING THE NEW MOON WITH NAKED EYE AND VALIDATING THE SIGHTING FOR ALL THE OTHER PLACES THAT SHARE WITH IT THE SAME NIGHT BUT MAKING A DISTINCTION BETWEEN THE OLD CONTINENT (EUROPE, AFRICA, ASIA AND AUSTRALIA) AND THE NEW CONTINENT (NORTH AND SOUTH AMERICA).
This is the fatwa of Ayatollah Muhammad Sa'id Hakim.
With prayers for your success.
You should follow the Marja of Taqleed and not the announcement of the government where you live. You dont need to disclose that you do not follow the government as Taqiyyah is Must on every believer.