Below, is an explanation on the bali tradition (animal sacrifice) based on the discourse of Pujayapad Puri Shankaracharyaji.
“Bali” means a gift or offering.
Śivavatāra Bhagavatpāda Śrī Ādi Śaṅkarācārya established four Āmanya pīṭhas (traditional centres) linked to four vedas. These pīṭhas are also Śakti pīṭhas. Hence, every pīṭha has a presiding devī. For example, Vimalā Bhagavati (who appeared from the navel of Mātā Sati) presides over Puri Pīṭha. In all the four pīṭhas established by Śrī Ādi Śaṅkarācāryaji, the offering made to devī is that of fruit, flowers, leaves, and not meat (hence, no bali or animal sacrifice).
When something is used (implied here, in a ritual) as per vedas and śāstras, its utilisation is not considered as a polluting factor, but takes the form of an adornment. Whatever is used (in the ritual) is also blessed (so if an animal is offered, it is also blessed). With this view the tradition of bali is also supported.
We must remember that the rice we consume is also living (immovable life form). In Śrīmadbhāgavatam it is written that a living being acts as the food of another living being. Hence, those who follow vāma-mārga and perform bali, are not creating any pollution and in fact, the act is seen as an adornment.
However, we (following Śrī Ādi Śaṅkarācārya’s parampara) do not perform bali. We only offer fruit, flower, leaves rice, vegetables, rice, roti. This is the method of worship of our path.
Tulasidāsji considered vāma-mārga as against the śruti. However, there were many debates of śāstra in Kashi and all those who claimed that vāma-mārga is not as per śāstras got defeated.
The conclusion was drawn that vāma-mārga is as per śāstras but sātvika people must not take its support.
In Manusmiriti it is suggested that gradually, if we can gain detachment, it is very good. There is a natural human liking towards intoxication, meat and sex. One must hesitate before indulging and gradually let go.
If detachment comes, it is very good and if one becomes vegetarian, even better!