Gemara

(Beraisa - R. Meir): One may not enter a city in which they serve idolatry, or go from it to another city;

Chachamim say, if the road also leads to another city, it is permitted.

If one's coins fell and scattered in front of idolatry, he may not bend to pick them up, for it would look like he bows to the idolatry. One may not put his mouth next to the mouth of a fountain (made in the image of a person) to drink, for it would look like he kisses idolatry. If it will not be seen, these are permitted.

Suggestion: 'It will not be seen' means that no one will see him.

Rejection: Rav Yehudah taught in the name of Rav that anything forbidden due to suspicion, is forbidden even in private! Rather, it means that that it will not seem like he bows or kisses.

Shabbos 146b (Mishnah): If one's clothes became soaked on the road, when he reaches the outer gate (of the entrance to the city, a guarded place), he spreads them out to dry in the sun, but not in front of people.

Question: According to Rav, it should be forbidden even in private!

Answer: Tana'im argue about this;

(Beraisa #1): One may spread them to dry, but not in public;

R. Eliezer and R. Shimon forbid.

64b - Question (Mishnah): A donkey may not go out with a bell, even if the clapper is plugged (it looks like the owner takes it to sell it in the market);

(Beraisa): One may plug up the clapper and take it in the Chatzer. (We are concerned for suspicion only in Reshus ha'Rabim.)

Answer: Tana'im argue about this (in Beraisa #1).

Kesuvos 60a (Beraisa - Nachum Ish Galya): If a gutter pipe became clogged (on Shabbos and the water is dripping into the house), one may covertly squash the clogging matter with his foot, without concern.

This is an unskillful way of fixing a Keli. (Normally, Chachamim forbid.) Chachamim did not decree when this will cause a loss.

(Rav Yosef): The Halachah follows Nachum Ish Galya.

Chulin 41b (Rava): The Mishnah permits to make a furrow near a pit and slaughter above the furrow, and the blood flows into the pit. One may not do so in the Reshus ha'Rabim, lest it encourage the Tzedukim.

A Beraisa says like Rava.

Rishonim

Rif and Rosh (Shabbos 62a and 22:9): Normally, we follow a Stam Mishnah against an argument in a Beraisa. However, in Avodah Zarah we asked from Rav (and answered). This shows that the Halachah follows Rav.

Rosh: Rav Nisim Gaon rules unlike Rav. A Beraisa (Chulin 41b) permits slaughtering above a furrow so the blood will flow into a pit, but not in Reshus ha'Rabim, lest he encourage the Tzedukim. This is no proof. Also here a Beraisa and Mishnah argue with Rav. Rav holds like the other Tana!

Note: In Chulin, also Rava holds unlike Rav, and he is Basra!

Rosh: We asked and answered similarly on 64b. Also, in Chulin one who sees will realize that he wants to clean his yard, so there is no suspicion at all. There is no proof from Nachum (Kesuvos 60a). There, there is no suspicion of an Isur mid'Oraisa, for people see that he unclogs it in an unskillful way. The Yerushalmi (Kilayim 40b) asks the Bavli's questions and other Mishnayos and Beraisos against Rav, and does not answer. If flax was dyed similarly to the color that wool is dyed, one may not make it a border for a wool garment (even if it is not connected in a way that the Isur of Shatnez applies) in a visible way, but one may do so for pillows and blankets. On Shabbos one may not pour into a sewage pipe that is covered for four Amos in Reshus ha'Rabim; a Beraisa permits pouring into a gutterpipe (that pours into the Chatzer), but not pipes that pour into Reshus ha'Rabim. It is permitted in winter, but Bar Kapara's Beraisa permits only in a covert place.

Rambam (Hilchos Shabbos 22:20): If one's clothes became soaked, he may not spread them out to dry, even in his house. This is a decree lest one say that he laundered on Shabbos, and now spreads the clothes to dry. Whatever Chachamim forbade due to suspicion is forbidden even in private.

Ran (Beitzah 4b DH mi'Chalon): In one version in the Gemara, Beis Hillel permit moving a ladder to an opening of a dovecote in Reshus ha'Yachid, but not in Reshus ha'Rabim, due to suspicion. The Rif omitted this, for he rules like Rav, that anything forbidden due to suspicion, is forbidden even in private. Rav Nisim Gaon brought proofs against Rav. On Chol ha'Mo'ed, one may make a laundry ditch or a coffin with the Mes in the Chatzer, but not in Reshus ha'Rabim (Mo'ed Katan 8b). I say that if these were difficult for Rav, the Gemara would have asked them, like it asked about coins scattered in front of idolatry. When the Mes is there, there is no suspicion! This is why the Yerushalmi permits even in the market if the Mes was famous.

Question (Shiltei ha'Giborim 62a:1): A Beraisa permits an animal to go with a bell in the Chatzer, but not in Reshus ha'Rabim. The Gemara, Rashi and Tosfos connote that it is like the Stam Tana who permits spreading clothes to dry in private, but Rav forbids. Hagahos Ashri explicitly says so. Why do the Rif, Rambam, Rosh, Tur (and Shulchan Aruch) rule like the Beraisa? They rule like Rav!

Answer (Magen Avraham 301:56): The Beis Yosef (336:9) says in the name of Tosfos that we forbid in private only when there is suspicion of a Torah Isur. However, why didn't the Gemara give this answer for Rav? Perhaps Tosfos rejects the Sugya in Shabbos and rules like the Sugya in Kesuvos. (The latter Sugya did not challenge Rav, for it holds that Rav's law is only when there is concern for a Torah Isur - Eshel Avraham.)

Poskim

Shulchan Aruch (OC 301:45): If one's clothes became soaked, he may wear them without concern lest he squeeze them. He may not spread them to dry, even in his house, lest people suspect that he laundered them on Shabbos.

Mishnah Berurah (161): This is whether they became wet through rain, or he fell in the river.

Kaf ha'Chayim (254): If the clothes fell in the river before he wore them, the Bach, Me'iri and Eshel Avraham permit to wear them. The Graz and Chayei Adam permit only if they became wet while he was wearing them.

Shulchan Aruch (ibid): It is forbidden even in private where no one will see.

Mishnah Berurah (165): It is forbidden even in private when there could be suspicion for an Isur mid'Oraisa, such as laundering.

Kaf ha'Chayim (261): Even when there is no suspicion of an Isur mid'Oraisa, one should not be lenient in front of his household.

Magen Avraham (55): The Shulchan Aruch connotes that we forbid only if they became soaked, but if a little water came on them one may spread them to dry, for there is no suspicion lest he laundered them. Some permit putting a little water on a garment on Shabbos (in Rema 302:9). However, the Shulchan Aruch (301:47) connotes even if they are slightly wet one may not spread them, for it forbids spreading even a sweaty garment.

Mishnah Berurah (163): Many Acharonim do not distinguish (and forbid even if they are only slightly wet).

Mishnah Berurah (164): One may hang up dirty diapers in the house or Chatzer. Since there is excrement on them, it is clear that he did not launder them. Perhaps we permit even if there is no excrement, if they are not totally soaked with urine, for people know that babies urinate in them. One may not spread them near an oven where it is Yad Soledes Bo.

Shulchan Aruch (ibid): It is forbidden only to spread them on Shabbos. If before Shabbos one spread laundry to dry, he need not remove it.

Mishnah Berurah (166): One who bathed on Erev Shabbos should spread the towel to dry before sunset. If he needs it on Shabbos, he may be lenient to spread it Bein ha'Shemashos.

Mishnah Berurah (167): This is even if they are spread where many see them. The primary suspicion is when he spreads on Shabbos, for there are grounds to believe that he lauddered them on Shabbos. Had he laundered them before Shabbos, he should have spread them to dry before Shabbos! Not everyone knows that they became soaked on Shabbos.

Kaf ha'Chayim (259): One may hang to dry hand towels or handkerchiefs if some filth is seen on them.

Kaf ha'Chayim (260): If he spread them on Shabbos, he need not take them down.