Gemara

12b (Reish Lakish): "V'Lo Yidbak b'Yadcha Me'umah Min ha'Cherem" forbids benefit from idolatry, but one may give benefit to it.

(R. Yochanan): Benefit from idolatry is forbidden, and all the more so giving benefit to it!

Question (Beraisa - R. Noson): When they exempt from tax anyone who dons a crown to honor the idolatry, one may not don a crown, for he benefits from idolatry! One may not buy without a crown, for he benefits the idolatry!

Answer (Rav Mesharshiya brei d'Rav Idi): Reish Lakish holds that Chachamim argue with R. Noson, and he rules like Chachamim. R. Yochanan holds that all agree with R. Noson.

51b (Mishnah): If there is a bathhouse or garden of idolatry, one may benefit from it Lo b'Tovah (without giving benefit), but not b'Tovah. If it belonged to idolatry and others, one may benefit b'Tovah and/or not b'Tovah.

Version #1 (Abaye): The Reisha forbids benefiting the priests of the idolatry. One may benefit commoners who serve it.

Version #2 (Abaye): The Seifa says, if it belonged to idolatry and others, one may benefit b'Tovah and not b'Tovah. I.e. he may benefit the others, but he may not benefit the priests.

Version #2 certainly agrees to the law of Version #1. If one may not benefit the priests even though they are not the sole owners, and all the more so when they are the sole owners!

Version #1 argues with the law of Version #2. If forbids benefiting the priests only if they are the sole owners, but permits when also owners own it.

Sanhedrin 74b (Rava): On their idolatrous festivals, Nochrim demand that we give to them Kelim with coals. Even though this pertains to idolatry, we are not Moser Nefesh! Since they intend for their own pleasure, it is permitted.

Rishonim

Rambam (Hilchos Avodah Zarah 7:17): If there is a bathhouse or garden of idolatry, one may benefit from it only Lo b'Tovah. If it belonged to idolatry and others, one may benefit even b'Tovah of the priests, as long as he does not pay rental.

Rosh (4:2): Rashi explains that 'b'Tovah' means that he pays. R. Tam disagrees. If so, it should have said 'for pay, or not for pay'! Above (44b), Rashi explained that he shows appreciation to the priests. It seems that one may grind and bake in a mill or over of priests for pay, but he does not show appreciation. Further, it seems that (Bach - even according to Rashi) one may pay, since the mill or oven is not in the Chatzer of the idolatry, like Afrodaiti's bathhouse. This is unlike a fair of Nochrim, in which one may not pay a tax to idolatry. There, the tax is for needs of the idolatry, i.e. decoration and sacrifices. Nowadays, it is a mere fixed stipend of the priests and their benefit. The money is not used for the idolatry. We give to Nochrim coals (for their rituals) because they intend for their own pleasure (Sanhedrin 74b). The Yerushalmi forbids eulogizing with flutes of idolatry or renting stores of idolatry. One may pay rent to the government, even though they use it for needs of idolatry. One may not give to Gaba'im of idolatry.

Ramban (51b DH Ha): Rashi explains that b'Tovah is when he pays. This is difficult. According to Version #2, how may we buy from them? One may not buy from a fair due to the tax! We can say that the tax is just to benefit the idolatry, but here he pays for what he buys. Some say that b'Tovah is showing appreciation, but he does not give anything. We say in Eduyos (5:1) that one eats Peros Shemitah only b'Tovah (to the owner of the land). This cannot mean for pay, for one may not sell Shemitah Peros! Rather, he thanks verbally. He must do so, lest he do so regularly. We hold like Version #2. One may not eat b'Tovah of the priests, but one may even pay others, even if they give part to priests.

Question (Ran 24a DH Kol): If the idolatry has difficulty selling the Peros, why is it permitted? Such a sale is the seller's benefit (Nedarim 31a)! It is forbidden regarding Mudar Hana'ah (one who may not benefit due to a vow), and all the more so regarding idolatry! Rather, b'Tovah is permitted, even if it means paying, for it is only a small Tovas Hana'ah, like one who buys for less, which we permit regarding Mudar Hana'ah (he does not benefit the seller, for the seller could have sold to another for more). He gives only a small benefit to idolatry. It is not Asur due to benefit from idolatry, for there is no Hekdesh to idolatry. Chachamim were stringent about idolatry when the priests get it all. The Ra'avad explains that b'Tovah is verbal. We forbid lest one be drawn after them. He supports this from Eduyos. This is no proof. Perhaps b'Tovah there is like here, so it is not considered business. The Yerushalmi is difficult. It connotes that we discuss full payment! This requires investigation. In practice, we rely on the Bavli. We rule like the latter version (#2). The Yerushalmi is like Version #1, which permits benefiting priests and others. Therefore, it permits renting flutes oid when they pay to the state. Since we hold like Version #2, it is forbidden. The Ramban permits when they collect for the state, even though people of the state give their share to idolatry. This requires investigation. Others say that b'Tovah of the priests is when they keep the money, and it does not go to idolatry. We forbid only because it appears wrong, therefore, we permit when also others receive. Our Gemara supports this. It connotes that priests are like the other worshippers, i.e. they profit, but the idolatry does not. The Yerushalmi connotes that even if the idolatry profits, it is permitted. Why do we permit when the item is hard to sell? Perhaps this is because we forbid such a sale regarding Mudar Hana'ah only mid'Rabanan, therefore we are not stringent when there are also others. The Rambam explains like the Ra'avad, and rules like Version #1. He holds that since verbal benefit is only mid'Rabanan, we are lenient. Also, Gemara explains Version #1 last.

Gra (YD 143:7): The Rambam rules like the first version whenever it says 'some taught...'

Beis Yosef (DH Kasav ha'Mordechai): The Mordechai (844) says in the name of Avi ha'Ezri that the Isur to give b'Tovas Hana'ah is when the seller would not have profited through anyone else. We may rent land and buy fruits from idolatry, for if not, many Nochrim would buy from it. On 13a we forbid benefiting idolatry. That discusses rose and myrtle, which are offered to it. A garden or bathhouse is to benefit the worshippers. R. Tam holds that the Isur to benefit idolatry is only near it, like the case of a garden and bathhouse. The Rashba (1:163) says that we follow the custom, which is like R. Tam. R. Peretz forbids benefiting the priests only when he rents from idolatry, but one may rent from the priests.

Poskim

Shulchan Aruch (YD 143:3): If there is a bathhouse or garden of idolatry, and the revenue goes to the priests, one may benefit from it only Lo b'Tovah. This is even if others have a share in the revenue with the priests. If the revenue does not go to the priests, rather, to its worshippers, one may benefit from it even b'Tovah, even if the bathhouse or garden belongs solely to idolatry.

Taz (5): Maharshal says that Lo b'Tovah is when no one gives to it. If others give, but they exempted him, he benefits from it! Whatever is Asur b'Tovah, one may not thank or pay for it. The Drishah asked, why may we buy (from priests) candles that extinguished? Even though they were Mevatel them, we benefit the priests! He answered that they were designated for this from the beginning. I do not understand this. Really, it is not difficult. The Isur is only when the priests receive a fixed stipend. Here, the candles were meant to be totally for the idol! It is a happenstance that they sell them. This is no worse than selling things unrelated to the idolatry, which is permitted.

Shach (6): The Levush says that 'Ovdeha' are those who work in the bathhouse or garden. This is wrong. Rather, it is is worshippers, like Rashi and the Ran say.

Rema: Some say that the Isur to benefit from it when the revenue goes to the priests is only if they stand in the Chatzer of the idolatry itself. If they do not stand in front of it, even though the revenue goes to the priests, one may benefit from it, unless the revenue goes to the idolatry itself. One may rely on this to be lenient.

Beis Yosef (DH Avodah): The Rambam rules like Version #1. The Rif and Rosh brought both versions and did not decide. Presumably, they hold like the latter version. The Ran rules like it, and it seems that also the Tur does. He forbids benefiting the priests along with others.

Shach (7): The Bach says that one must be stringent if no one else would have bought the Peros or bathed in the bathhouse.