After a discussion on one of my previous questions here True purpose of celebrating Eid-Al-Adha, I wanted to validate/confirm that if someone chooses to follow Shafi'i Madhab, then he/she can choose not to sacrifice an animal on the occasion of Eid - Ul- Adha and still be a good Muslim, right? Please confirm.
Short answer: you can safely omit performing the sacrifice at 'id al-Adha, and be a good Muslim, but you'll miss a lot of rewards.
The majority of scholars actually say that sacrifice on 'Id al-Adha is a highly recommended sunnah (sunnah mu'akkadah) for a person who can offered its costs, this is the view of imam a-Shafi'i and the most famous view of both imam's Malik and Ahmad. And also the view of many sahabah, many of the tabi'yn and scholars like Sufyan a-Thawri, ibn al-Mubarak and abu Thawr...
However on the other hand it is regarded as wajib by abu Hanifa, al-Awza'y, al-Laith ibn Sa'ad, and an in another view of mam Ahmad and regarded as the madhhab of Malik (scholars of this madhhab rather favored this, this might be due to a statement of Malik which goes beyond having one sacrifice per family).
We could investigate whether wajib in this context means it is obligatory especially in case of the hanafi school of fiqh, since they have a slight difference between wajib (more like a sunnah mua'kkadah) and fard (obligatory). But a difference of opinion in which both parties have clear evidences means that one could rather safely take the more lenient view, since the sahih hadith suggests that doing the sacrifice is a matter of choice:
If anyone of you intends to offer sacrifice he should not get his hair cut or nails trimmed. (Sahih Muslim)
Further it is mentioned that abu Bakr, 'Omar and many other sahabah omitted the sacrifice to avoid that people may think it is ordered. Reports stating this are recorded for sahabah like ibn 'Abbas, ibn 'Omar, abu Mas'ud al-Anasari.
Nevertheless temporary scholars tend to say that the stronger of both views is that it is a sunnah mu'akkadah meaning that not acting upon it doesn't mean one would commit a sin, but one would be missing a good deed and a lot of thawab. In other words it is very highly recommended especially if done in the manner practiced by the prophet () and early Muslims meaning to feed a part of it to those in need to give them a reason more for celebrating the 'Id and observe many other good deeds on the day of 'id and the following days.
The scholars (may Allah have mercy on him) differed with regard to the ruling on udhiyah: is it obligatory or Sunnah mu’akkadah (a confirmed Sunnah)? The correct view is that it is Sunnah mu’akkadah for the one who can afford it, but there is no sin on the one who does not do it.
(islamqa fatwa #145105)
Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on him) said: “Udhiyah is Sunnah mu’akkadah for the one who is able to do it, so a person should offer the sacrifice on behalf of himself and the members of his household.” (Fataawa Ibn ‘Uthaymeen, 2/661)
(islamqa fatwa #36432)