Gemara

(Beha citing R. Yochanan): Muktzeh (an animal designated for idolatry) is forbidden only after it is fed vetch (horsebean) of idolatry.

30b (Mishnah - R. Chanina ben Antigionus): If a Kosher calf nursed from a Terefah, it may not be offered.

31a - Suggestion: He forbids because it was fattened by the Tereifah's milk.

Rejection: If so, we should forbid an animal that ate vetch of idolatry (even if the animal was not designated for idolatry)!

(R. Chanina Trita'ah): Rather, he forbids a calf that nursed (from a Tereifah) every morning, for this is enough to sustain it.

Rishonim

Perush ha'Mishnayos and Bartenura (Temurah 6:5): The Mishnah forbids a Kosher animal that nursed from a Terefah only the day it nursed, for the milk can sustain it for 24 hours, and digestion is not finished until 24 hours. After it was digested, even if it was fattened excessively with vetch of idolatry, all permit it. The Halachah does not follow R. Chanina.

Tosfos (31a DH she'Yankah): Likewise, if an animal ate vetch of idolatry it is forbidden, for it grew primarily from Isur. It seems that it is forbidden even to people.

Mordechai (Yevamos 65): If a Kohen rented a cow from a Yisrael, even though he must feed it, he may not feed it vetch of Terumah. This is difficult, for a Yisrael may benefit from Terumah! A Mishnah (Eruvin 26b) permits a Yisrael to use Terumah to make an Eruv! R. Tam answered that a Yisrael may not benefit from Terumah in a way that consumes it. R. Yakir answered that one may not feed it Terumah, for if it is fattened through Terumah, (after it is slaughtered) the Yisrael who eats it, he eats Terumah. This is difficult. If so, why may we eat chickens fattened through eating Sheratzim?

Poskim

Rema (YD 60:1): If a (Kosher) animal was fattened with Isur, it is permitted, unless it was fed only Isur its entire life.

Toras Chatas (of the Rema, 65:10): Isur v'Heter says that if a (Kosher) animal nursed from a Tamei animal, surely it is permitted, just like chickens fattened through eating Sheratzim. However, if the matter is known, one should not buy it, due to Mar'is ha'Ayin. Also the Mordechai permitted chickens that eat Sheratzim. However, Tosfos forbids if it was fattened only with Isur its entire life. The same applies to a Kosher animal that nursed from a Terefah or Temei'ah.

Minchas Yakov (16): This connotes that all the more so, l'Chatchilah one may not feed it Isur. The Shach (below) says that the Mordechai permits, and he agreed.

Minchas Yakov (18): If it grew primarily from Isur, it is as if it was fed Isur its entire life. Mas'as Binyamin (Chidushei Dinim l'Yoreh De'ah 3) says so.

Shach (5): Isur v'Heter forbids l'Chatchilah to buy an animal that nursed from a Tamei animal. It seems that he forbids even if it did not nurse Tamei milk its entire life. If so, all the more so one may not feed it forbidden food. This is like 142:11, in which we permit a cow fattened with vetch of idolatry only b'Di'eved, due to Zeh v'Zeh Gorem. However, the Mordechai (Yevamos 66) permits feeding it Isur l'Chatchilah. It seems that he permits this its entire life. This is unlike a cow fattened with vetch of idolatry, for one may not benefit from idolatry, but one may feed it Isur that is Mutar b'Hana'ah, for one does not eat the Isur itself. This is even if it ate Isur its entire life. We do not distinguish fattening from basic food needs. Surely, 'its entire life' is not precise. It means most of what it ate.

Minchas Yakov (17): Presumably, the Shach is correct, that Tosfos forbids only regarding Isurei Hana'ah. Eichah Rabsi 1:1 supports this.

Note: It discusses four Yerushalmiyim who went to Athens. A host gave them meat and wine. Afterwards, Ploni (a guest) mentioned that the meat had the taste of a dog. The host found that the lamb he fed them had nursed constantly from a dog. Etz Yosef explains that surely the host was a Yisrael, for the guests would not eat meat and wine of a Nochri. (Likewise, Ploni would have immediately ceased eating the meat if it were forbidden.) However, Yefei Anaf connotes that the host was a Nochri. If so, in any case Ploni knowingly transgressed, so there is no support from the Medrash.

Sifsei Da'as: The Shach proved that not all agree that if it was fattened its entire life only Isur, it is forbidden. It seems that the Rema equates the Mordechai to Tosfos. The Mordechai discusses when it ate also other things, and Tosfos discusses when it ate only Isur. However, this is not so. Isur v'Heter forbids buying it l'Chatchilah, due to Mar'is ha'Ayin. This is correct, for Zeh v'Zeh Gorem is forbidden l'Chatchilah, just like a cow that ate vetch of Isur. This is even if it was not its entire life. If so, why would the Mordechai permit l'Chatchilah (if it was fattened a little through Isur), if when it was fattened its entire life it is forbidden even b'Di'eved? It is forbidden l'Chatchilah, due to Zeh v'Zeh Gorem! Rather, the Mordechai permits even if it was fattened its entire life, unlike Tosfos, for it is not an Isur Hana'ah, and the Isur is not intact. It was digested. If it was fattened its entire life through Isurei Hana'ah, then it is forbidden even b'Di'eved. If it ate Isurei Hana'ah and Heter, it is forbidden l'Chatchilah due to Zeh v'Zeh Gorem. Isur v'Heter permits even if it grew primarily through Isur, and all the more so if it ate Isur only every morning, b'Di'eved it is permitted, for the Isur was digested. He forbid due to Mar'is ha'Ayin, lest people say that Zeh v'Zeh Gorem is permitted l'Chatchilah. All the more so if it ate Isur its entire life (it is forbidden, but only due to Mar'is ha'Ayin). This is unlike Tosfos. The Mordechai holds like Isur v'Heter regarding the Heter after it was digested, but he permits l'Chatchilah without concern for Mar'is ha'Ayin, unlike Isur v'Heter. If it ate Isurei Hana'ah its entire life it is forbidden even b'Di'eved. If it ate also other things, it is permitted b'Di'eved due to Zeh v'Zeh Gorem. Tosfos connotes that there is no difference between whether this was its entire life. Tosfos explains R. Chanina, and he forbids even if it nursed only every morning.

Sifsei Da'as: Tosfos discusses an animal that eat vetch of Isurei Hana'ah. If not, what was Tosfos' Chidush that forbidden vetch is like nursing from a Terefah? Tosfos was unsure whether it is forbidden to people if it ate Isurim that are not Isurei Hana'ah. We must fix the text of Rashi (31a DH Hachi) to say that the Isur is due only to Muktzeh. If not, it is permitted. Since the Isur is only to the Mizbe'ach, it is permitted to people. Do not say that the Mishnah teaches the leniency of Chachamim (that they permit even if it ate Isurei Hana'ah). The Mishnah did not mention Chachamim! In summary, if it ate an Isur Achilah (but not Isurei Hana'ah), perhaps all permit b'Di'eved even if it ate its entire life. If it is known, l'Chatchilah it is forbidden due to Mar'is ha'Ayin. Similarly, one may not feed Isur to birds (if he will eat the birds). If it ate Isurei Hana'ah its entire life, it is forbidden b'Di'eved. Tosfos was unsure if it ate only every morning. L'Chatchilah we buy geese that eat worms in water. This does not make it Zeh v'Zeh Gorem. Also Yisre'elim may do so sometimes! (Perhaps he means that one may eat worms if their initial creation was in a Kli, like it says in Chulin 66b - PF.)

Gra (1): In Temurah, we brought a source to disqualify for a Korban a cow that ate vetch of idolatry. This connotes that one may eat it. Tosfos was unsure. Perhaps this is when it ate also other things, but if not, one may not eat it, like it says in Avodah Zarah 49a. The Gemara said that it nursed every morning, i.e. but it also ate Heter. However, the Sifri permits a calf of a Tereifah (to people) only if it nursed also from a Kosher animal. (If it nursed only Isur, it is forbidden to people.)

Mishnah Berurah (488:33): If an animal ate Chametz b'Pesach, the Pri Megadim permits what is milked from it more than 24 hours later. Some are lenient even during the same day if it eats Chametz in the morning and Heter at night.

Igros Moshe (OC 1:147 Anaf 7 DH v'Hinei): If animals or birds were fattened through Chametz during Pesach or any Isur Hana'ah, even if they did not eat Heter, one may eat them that day. Also the milk is permitted, even if it is a Yisrael's animal. Even though the owner transgressed Bal Yera'eh and benefit from Chametz, this does not forbid the animal or milk. This is letter of the law. A Ba'al Nefesh should be stringent not to consume milk or a bird fattened only through Chametz. Stam (if one does not know), even a Ba'al Nefesh need not be concerned. Likewise, one need not be concerned for a Nochri's animal that ate Chametz, even according to the Rema.