Gemara

57a (Beraisa): If a Nochri measured (the depth of) wine by sticking in his hand or foot, one may sell the wine;

R. Noson says, if he stuck his hand in, one may not benefit from it.

A Nochri climbed a date tree and took a Lulav. On his way down, the Lulav accidentally touched wine. Rav ruled that the wine may be sold to Nochrim.

Rav Kahana and R. Asi: You yourself said that a one day old Nochri makes Yayin Nesech (if he touches wine, even though he has no intention)!

Rav: I meant only that one may not drink it. One may benefit from it.58a: R. Yochanan ben Arza and R. Yosi ben Nehorai were drinking wine. A man came; they offered him to drink. After he poured from the bottle into his cup, they realized that he was a Nochri. One Chacham forbade the bottle.

R. Yehoshua ben Levi: He held that the Nochri was not Menasech, for he assumed that it is beer (they would not invite a Nochri to drink wine).

59b: A Nochri's Esrog fell into a barrel of wine; he ran and stuck his hand in to retrieve it. Rav Ashi told Yisraelim 'hold his hand so he cannot shake it, and tilt the barrel so the wine will flow out.'

(Rav Ashi): If a Nochri b'Mezid was Menasech Reuven's wine, Reuven may ask him for its full (initial) value.

This is not considered benefit from Yayin Nesech. The Nochri forbade it to Reuven, as if he burned it. Reuven collects payment for the damage.

64b: Rav Yehudah sent a gift to Avidarna, and Rava sent a gift to Bar Shishach on the Nochri festival. They reasoned that this is permitted, for these Nochrim do not serve idolatry.

Rishonim

Rif (27a): Chachamim did not decree about Ko'ach (impetus) of a Nochri (that moved wine) without intent. One may even drink the wine.

Rambam (Hilchos Ma'achalos Asuros 12:5): If a Nochri touched wine without intent, one may only benefit from it, e.g. if the Nochri fell on a flask of wine or put his hand in thinking that it is oil, and it was found to be wine.

Rambam (9): If a Nochri used a reed to measure the pit holding the wine, or he chased a wasp from the wine with a rod, one may only benefit from it.

Rosh (4:7): The Rashbam and Rivan cite Rashi in the name of Ge'onim that nowadays one may benefit from wine of Yisrael that Nochrim touched, for they are not normally Menasech. They are like Nochrim ignorant of idolatry, i.e. children, and they forbid only drinking, but not Hana'ah. In many places people rely on this to take Yayin Nesech from Nochrim for their debts. Also, if a Nochri touches a Yisrael's wine, he sells it to Nochrim. The Ri disagrees. Rav says that a Nochri baby does not forbid Hana'ah, but this is not because he is not proficient in idolatry and Meshamshim. If it were, he would permit even drinking! Rather, it is because he did not intend to touch. The Gemara compares this to touching wine without intent. If so, nowadays Nochrim forbid Hana'ah, for they intend to touch. Intent to touch without intent for Nisuch is more stringent than no intent at all. If a Nochri touched wine through a Lulav without intent, one may drink it. If he measured with a reed or chased a wasp, i.e. intent to touch without intent for Nisuch, one may not drink the wine. Similarly, we can say that one may benefit when there was no intent to touch, but not when he intended to touch without intent for Nisuch. Do not distinguish and say that we forbid one who measured with a reed without intend for Nisuch lest he come to be Menasech, but nowadays Nochrim will not come to be Menasech. We do not rely on poor answers to permit Hana'ah from wine that Nochrim touched. The only Heter we find is like Rav Ashi said, to collect from the Nochri who touched it, or the Nochri can sell it to other Nochrim. It is as if he sells it for his own needs.

Hagahos Ashri: One may not leave it in his house to grow old (old wine is worth more). One may not do so even in the Nochri's house. We permit Hana'ah, but one must distance (from it) as much as possible.

Rosh (ibid): Perhaps those who are lenient rely on Chachamim of R. Noson, who permit selling wine even if the Nochri measured with his hand. Nowadays, touching of Nochrim is like measuring. Also, their touching cannot lead to Nisuch. However, it seems that the Halachah follows R. Noson. The case of the Esrog that fell into wine supports this. Rav Ashi commanded to hold his hand, lest he shake it while pulling it out, even though he intended only to retrieve his Esrog. Perhaps this is even like Chachamim. Removing an Esrog is less distracting than measuring wine. Also, even though the wine would be Asur b'Hana'ah had they not held his hand while he retrieved his Esrog, nowadays we can permit because Nochrim do not intend to shake at all, and they are not Menasech at all. This is like Giluy (things left exposed). We are not concerned for Giluy nowadays, for snakes are not found among us. This is not a solid proof, for Nisuch was forbidden through a Minyan (vote of Chachamim). Another Minyan is needed to permit it, even though the reason no longer applies. Giluy was forbidden due to danger, only where there is danger. There are many things we are not careful about, for we rely on "Shomer Pesa'im Hash-m" (Hash-m guards people who do not know to guard themselves). A proof to permit today is from Rav Yehudah and Rava, who sent gifts to Nochrim on their festivals, for they knew that they do not serve idolatry and will not thank idolatry. The first Mishnah of our Masechta did not distinguish, and it was forbidden through a Minyan! Rather, from the start they decreed only about Nochrim who serve idolatry. Likewise, Yayin Nesech was decreed only about such Nochrim. This permits only wine of Yisrael that Nochrim touched, but their Stam wine is Asur b'Hana'ah due to intermarriage. There is no reason to permit this. However, we can say that at first they forbade only drinking it, just like their bread, oil and cooked foods, and because they used to be Menasech they forbade Hana'ah, like wine offered to idolatry. Nowadays it suffices to make wine like oil and cooked foods. There is no clear proof to permit Hana'ah. It is better that Yisrael be Shogeg than Mezid.

Tosfos (57b DH Le'afukei): R. Tam says that nowadays Nochrim are like children, so they forbid only benefit from our wine, like Rav. The Ri proved from the case of the Lulav that an adult who intended to touch wine without intent for Nisuch is more stringent than a baby who had no intent to touch. R. Tam retracted and said that the only clear Heter Hana'ah is to sell it to the Nochri who touched it. A case occurred, and his father R. Meir overtly destroyed the Yayin Nesech. R. Tam did not forbid, since the custom is to be lenient. It is better that Yisrael be Shogeg than Mezid. A support is that R. Noson forbids one who measured by hand only lest he shake and be Menasech. He would agree nowadays that shaking is not Nisuch. One who is stringent will be blessed.

Poskim

Shulchan Aruch (YD 124:24): If a Nochri touched wine through something else without intent, e.g. his Lulav or garment touched wine without intent, or he intended to touch through something else, but he thought that it is not wine, one may even drink the wine.

Rema: Nowadays, the nations are not idolaters, so whatever they touch is called without intent. Therefore, if he touched wine through something else, even if he knew that it is wine and intended to touch, one may even drink it, for this is called touching through something else without intent. We similarly permit if he touched with his hand without intent to touch, or he did not know that it is wine. One should not publicize this in front of an ignoramus.

Beis Yosef (DH Kasav, citing Mordechai 847): R. Tam permits what a Nochri touched through something else when he thinks that it is beer. If so, nowadays that Nochrim are not Menasech, and are not proficient about idolatry and Meshamshim, they are like a baby, so he would permit what a Nochri touched through something even if he knew that it is wine, since he is not Menasech and will not come to be Menasech.

Taz (30): If the Nochri intended to touch but he was distracted with one of the matters in this Siman, one may not drink the wine. We learn from one who measured, like the Rosh said. Also the Rambam connotes that for touching by hand, distraction is worse than no intent. He permits Hana'ah if a Nochri put his hand in thinking that it is oil, yet he permits if a Nochri measured (only) through a reed, i.e. but not by hand. Also the Beis Yosef explains the Rambam like this. It seems that he permits even drinking if the Nochri touched through something else without intent, like the Rif and R. Tam. If he forbade like Rashi, he should have taught about touching through a reed by accident or when he thought that it is oil. Touching by hand forbids Hana'ah if he intended, and forbids drinking if he did not intend. Why didn't the Beis Yosef bring the Rambam's Heter to drink?

Shach (71): The Darchei Moshe and Bach connote that whenever the Gemara forbids only drinking, we permit drinking. Also the Mizrachi and Ben Chaviv say that we are one level more lenient than the Gemara. However, we hold (123:1) that if it will not entail a loss, even nowadays Nochrim are considered idolaters. The Rema and Bach there agreed. Maharil (38) permits what a Nochri touches without intent nowadays only to avoid a big loss. The Rema and those who follow him did not cite the Maharil. Perhaps they would have admitted had they seen his Teshuvah. Also, this leniency is not found in the famous Rishonim or Acharonim. One may be lenient in any case when letter of the law it is permitted, e.g. a minor.