The Gemara in Masechet Shabbat (147) prohibits one to "Men’aer Talito"-shake out his garment on Shabbat. There is major disagreement how to understand this Gemara. Rashi understands that the Gemara is talking about shaking dust out of a new garment, which violates the Torah prohibition of laundering. Other Rishonim (early authorities) interpret the Gemara as referring to a case of shaking out water, not dust, from a garment. For example, someone left his jacket outside on the porch overnight, and in the morning wants to shake out the dew so that he can wear it to shul.
Maran (302:1) records the Halacha as a prohibition of shaking dew out of a new, dark garment. Apparently, he holds like the Rishonim who disagree with Rashi. Accordingly, it can be inferred that there is no problem of shaking out dust, according to Maran. The Rama brings the opinion of Rashi and says that one should not shake out dust.
Therefore, according to the strict letter of law, Sepharadim may shake dust out of a garment, whereas Ashkenazim should be strict. However, The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) in Parshat Vayehi was strict, like the Rama, since there is an issue of a "Chiyuv Hatat," a Torah Prohibition. Even though Hacham Ovadia and Hacham Ben Sion hold that according to the letter of the law Sepharadim may be lenient, nevertheless they ruled that one shake off dust with a "Shinui" (in an abnormal fashion), such as using one’s sleeve as opposed to directly with his hand. Hacham Ovadia writes that one who refrains from using a hat brush to remove dust "Tavo Alav Beracha" (is praiseworthy). Therefore, one should be careful to hang up and store his clothes in a proper place so that they will not become dusty and need cleaning.
According to all opinions, there is no problem brushing a feather of a garment. As opposed to water and dust, which are absorbed in the fabric, the feather merely rests on top of garment.
If clothing became soaked with rain, one should be very careful not to shake it out. Rain is even more of a problem than dew, because besides for the violation of Libun-(laundering), it also presents an issue of Sechita (wringing). However, this restriction does not apply to a rain poncho or nylon slicker, in which the droplets rest on the surface, and are not absorbed. It is no different from the case of the feather.
Not only is it prohibited to shake out a wet garment, but also one may not hang it up in a place clearly designed for drying clothes. This presents a problem of Marit Ayin, whereby onlookers might assume that the garment was laundered in violation of Shabbat. However, Shemirat Shabbat K’Hilchato (Rabbi Yehoshua Neuwirth, Jerusalem, 1927-1913) points out that this restriction does not apply to raincoats. It is clear that it became wet from rain, and no one will think that it was laundered on Shabbat.
SUMMARY
It is prohibited to shake dew out of a new, dark garment on Shabbat.
Sepharadim may shake off dust from a garment with a Shinui.
It is prohibited to shake rain out of any soaked garment.
It is permitted to shake a feather off a garment.
