Does Anushasan Parva, chapter 88 of the Mahabharata, allow cow sacrifice?
Yes, Bhishma does say that in chapter 88 of the Anushasana Parva of the Mahabharata:
Listen to me, O Yudhishthira, what those Havis are which persons conversant with the ritual of the Sraddha regard as suitable in view of the Sraddha and what the fruits are that attach to each. With sesame seeds and rice and barley and Masha and water and roots and fruits, if given at Sraddhas, the Pitris, O king, remain gratified for the period of a month. Manu has said that if a Sraddha is performed with a copious measure of sesame, such Sraddha becomes inexhaustible. Of all kinds of food, sesame seeds are regarded as the best. With fishes offered at Sraddhas, the Pitris remain gratified for a period of two months. With mutton they remain gratified for three months and with the flesh of the hare for four. With the flesh of the goat, O king, they remain gratified for five months, with bacon for six months, and with the flesh of birds for seven. With venison obtained from those deer that are called Prishata, they remain gratified for eight months, and with that obtained from the Ruru for nine months, and with the meat of the Gavaya for ten months. With the meat of the buffalo their gratification lasts for eleven months. With beef presented at the Sraddha, their gratification, it is said, lasts for a full year. Payasa mixed with ghee is as much acceptable to the Pitris as beef. With the meat of the Vadhrinasa the gratification of the Pitris lasts for twelve years. The flesh of the rhinoceros, offered to the Pitris on the anniversaries of the lunar days on which they died, becomes inexhaustible. The potherb called Kalasaka, the petals of the Kanchana flower, and meat of the goat also, thus offered, prove inexhaustible.
Pitris are spirits of departed ancestors, by the way. In any case, see my answer here for the moral justification of animal sacrifice.
Also, it should be noted that the Brahma Vaivarta Purana says that offering meat at the Shraddha ritual is not permitted in the Kali Yuga:
In this Age of Kali, five acts are forbidden: the offering of a horse in sacrifice, the offering of a cow in sacrifice, the acceptance of the order of sannyāsa, the offering of oblations of flesh to the forefathers, and a man’s begetting children in his brother’s wife.
Now like many verses in the Brahma Vaivarta Purana, some consider this verse to be an interpolation. But this is a moot point, because pretty much no one offers meat in Shraddha nowadays; they use one of the options referred to by Bhishma that don't involve meat.
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