One issue that the foremost Aḥaronim dealt with is the status of milk which came from a cow that ate ḥametz. Clearly the milk itself does not contain ḥametz, for it was digested and completely transformed to the point that it is no longer considered ḥametz at all. However, the cow was able to produce milk by virtue of the ḥametz, and since it is forbidden to derive benefit from ḥametz, perhaps it is forbidden to benefit from milk produced by the virtue of ḥametz.
The poskim agree that milk obtained from a cow before the onset of the prohibition of ḥametz is kosher for Pesaḥ, because one is allowed to derive benefit from ḥametz before Pesaḥ. Just as it is permissible to sell ḥametz before Pesaḥ and use the money to buy food for Pesaḥ, so too it is permissible to feed a cow ḥametz before Pesaḥ in order to produce milk that will be consumed on Pesaḥ.
The dispute concerns milk from a gentile’s cow that ate ḥametz after the onset of the prohibition. Some are lenient, contending that since the ḥametz prohibition does not apply to the animal of a gentile, its milk is not considered produced in a forbidden manner. Furthermore, ḥametz alone does not cause milk to be produced. Rather, it must be combined with other foods and the animal’s biological processes. Since the ḥametz is only one factor, it is not prohibited. Against them, some poskim rule stringently that as long as ḥametz is a factor causing production of milk, the milk is forbidden. Others say that if 24 hours elapsed between the eating of ḥametz and the milking, the milk is kosher.
If an animal owned by a Jew was fed ḥametz in violation of halakha, one must be strict and not drink its milk, firstly because it is forbidden for the animal’s owner to derive benefit from ḥametz, and secondly because one may not assist those who violate the Torah. The same applies to eggs and meat.
During Pesaḥ, Tnuva, a major Israeli dairy producer (and perhaps others) only accepts milk from dairy farms that have been made kosher for Pesaḥ and whose cows are not fed ḥametz. In this case, it is unnecessary to be scrupulous and buy milk products before Pesaḥ, because even dairy products manufactured on Pesaḥ are completely kosher for the duration of the holiday.
However, MA 445:5 (as well as Taz) states that due to the stringency of ḥametz, which renders mixtures forbidden even in the smallest quantity, something produced by ḥametz and another factor is forbidden. Nevertheless, most poskim, including SA, Shakh, and Gra, maintain that even in the case of ḥametz “zeh ve-zeh gorem” is permitted. SAH (445:10 and Kuntrus Aḥaron) concludes that the consensus of most poskim is to be lenient, and one may certainly be lenient in a situation of significant loss or an extenuating circumstance. This is also the view recorded in BHL 445:2.
Some, however, argue that regardless of one’s position on zeh ve-zeh gorem, milk from a gentile’s cow that ate ḥametz is permitted. As explained in Beit Ephraim, OḤ 35 (cited in Sha’arei Teshuva at the end of §448), since ḥametz is permissible for a gentile on Pesaḥ, we do not view the milk from his cow as having been produced by something from which one is forbidden to benefit. Nishmat Adam §9 permits on different grounds: MA’s stringency only applies when the ḥametz is intact, unlike in the case of the milk. Responsa Mahari Aszod §127 and Responsa Maharam Schick §§212 and 222 rule likewise. Igrot Moshe OḤ 1:147 states that even if the gentile feeds his cow only ḥametz, its milk is permissible even according to the strict opinions.
On the other hand, Pri Megadim (in Eshel Avraham on §448) is concerned about causing benefit that derives from ḥametz. Thus, there is still uncertainty if less than 24 hours passed between when the cow ate ḥametz and the milking (if more than 24 hours passed, the milk is permissible). Yeshu’ot Yaakov also states that one should preferably use milk that was extracted from the cow more than 24 hours after the cow ate ḥametz, but if less than 24 hours passed, the milk is still permissible as long as the cow ate permissible foods in addition to the ḥametz (because of zeh ve-zeh gorem; see MB 448:33). Some authorities ruled stringently: Kitzur SA 117:13 cites both opinions and concludes: “One who guards his soul should be strict, and especially in places where the prevalent custom is to be stringent, God forbid one should be lenient.” Arugat Ha-bosem 2:138 states that even according to those who permit the milk, a righteous person (“ba’al nefesh”) should refrain from drinking it, since it has negative spiritual effects. Ben Ish Ḥai (Year One, Tzav 42) states that one should not drink milk from a gentile’s cow out of concern that the gentile fed it ḥametz. R. Ḥayim Palachi writes similarly in Ru’aḥ Ḥayim 448:1.
If the cow ate ḥametz before the ḥametz became prohibited and was milked after the ḥametz became prohibited, the vast majority of poskim maintain that the milk is kosher for Pesaḥ. Sdei Ḥemed mentions the opinion of Rinun Yitzḥak forbidding the milk of a cow that ate ḥametz before Pesaḥ and was milked after the ḥametz became forbidden, and states that this goes too far, since all other poskim say that this milk would be permissible. Nonetheless, because of this opinion some act stringently and only purchase dairy products before Pesaḥ. Sdei Ḥemed expands this topic in Ma’arekhet Ḥametz U-matza 2:4, and see Kaf Ha-ḥayim 448:113 as well.
. According to Nishmat Adam and Igrot Moshe OḤ 1:147, if a Jew feeds his animal ḥametz on Pesaḥ, the animal’s milk is kosher for Pesaḥ. Nonetheless, many others are stringent, not only because of zeh ve-zeh gorem, but because the Jew assists in the violation of a prohibition (“mesayei’a”). In fact, I heard from R. Weitman, the rabbi of Tnuva, that all dairy products produced on Pesaḥ are made from the milk of cows that did not eat ḥametz, so that the milk will be acceptable to everyone and can be bought on Pesaḥ. Another potential problem was that straw and possibly some grain might stick to the cows’ bodies as they wallow in mud, and these grains might accidentally get mixed into the milk. If the milk was produced before Pesaḥ, the taste of the grain is batel be-shishim even if it found its way into the milk, and since this is a liquid mixture even Rema (447:4) would agree that the taste of the ḥametz is not ḥozer ve-ne’or. If the grain fell into the milk on Pesaḥ, however, it is not batel. Although in the present case it is uncertain that any grain fell in, it would nevertheless be commendable to buy dairy products before Pesaḥ. However, I heard from R. Weitman that Tnuva introduced the practice of filtering all the milk very thoroughly right after the milking, so that no grain that falls in would have enough time to flavor the milk. Thus, one may purchase dairy products on Pesaḥ even according to the strictest opinions.