The First of Dhil-Hijjah
Question :

If the government of Saudi Arabia announces the first of Dhil-Hijjah to be on a particular day, which does not conform to the religiously-established day, can he perform the Hajj according to the government-announced date?

Answer :

If the current authorities of the two holy mosques permit Muslims from all sects to perform their Hajj based on the teaching of their own sects, then one must follow what the religious evidences prove in determining the time to perform the Hajj accordingly.
If the authorities have enforced a set day, then it is acceptable to perform the rites of Hajj accordingly.