All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is not a condition that Muslims stop working on the days of ‘Eed (Adha or Fitr). However, it is a recommended Sunnah that they perform the ‘Eed prayer. The Hanafi School is of the view that it is obligatory on all Muslims to perform the ‘Eed prayer. The Hanbali School is of the opinion that the ‘Eed prayer is not an individual obligation, but it is a communal one. This means that if some Muslims in a given area perform it, the remaining Muslims in that area are exempted from the obligation of performing it [and exempted from sin]. However, if it is not performed at all, then all the Muslims in that area are sinful.
But the most sound and correct opinion is that the ‘Eed prayer is a recommended Sunnah and this is the opinion of Maalik and Ash-Shaafi’i. It is desirable for Muslims to show happiness on this day and make large meals for their families. There is no objection that some parties are held on the second and third day of ‘Eed. None of this rules out working on this day. But, know that it is unlawful for Muslims to participate in the celebrations of non-Muslims festivals.
For more benefit, please refer to Fatwa 83628.
Allah knows best.