The custom of kaparos is the subject of a long-standing controversy. This waving of chickens over people’s heads in a repentance ritual before Yom Kippur, leading to the chicken’s slaughter, has engendered significant opposition over centuries. Great authorities like the Ramban and Rashba attempted to end this practice that they found religiously objectionable, even pagan. R. Yosef Karo, in Shulchan Arukh (Orach Chaim 605:1) also opposed it. However, the custom continues with great popularity and the support of many authorities (e.g. Rema, ad loc.).
Even today the practice is still mired in controversy. Animal rights advocates object to the mistreatment of chickens prior to the ritual. When I lived near what became the central Flatbush location for kaparos, I saw first hand the terrible treatment of the chickens before, during and after the ritual. There is much about which to object.
Some people substitute money for the chicken, waving cash overhead in a symbolic self-calling for repentance. I suspect that this waving a relatively small amount of money makes much less of an impact than seeing a live animal go to its death, as we eventually will for our sins unless we repent. Given the substantive historical opposition to the practice, I see great precedent for stopping it entirely.
I recently learned that R. Joseph B. Soloveitchik did not observe this custom. His son-in-law and leading student, R. Aharon Lichtenstein, reports that his family had long thought that no Brisker, steeped in Talmudic rationalism, would ever tolerate such a custom. He was surprised when he entered the home of a leading Jerusalem Soloveitchik on the day before Yom Kippur and discovered chickens in the house for kaparos. The family debated whether the rabbinic head of the home actually practiced kaparos or merely pretended to do so (Mevakshei Fanekha, p. 245).
That a leading rabbinic authority refused–that is the impression R. Lichtenstein gives–to practice such a custom should not be surprising. Not only has objection to it been sustained over centuries but, as Arukh Ha-Shulchan (ad loc., par. 5) states, rabbinic authorities actively tried to abolish the practice. Only popular devotion prevented their success.
I sometimes hear calls from animal rights advocates that people substitute money for chickens in the kaparos ritual. They would be equally, perhaps more, justified in encouraging people to drop the practice altogether.