I hadn't known this until today, but L.A. apparently has an unconstitutional ban on animal sacrifice, in Municipal Code § 53.67:
(a) No person shall engage in, participate in, assist in, or perform animal sacrifice.
(b) No person shall own, keep, possess or have custody of any animal with the purpose or intention of using such animal for animal sacrifice.
(c) No person shall knowingly sell, offer to sell, give away or transfer any animal to another person who intends to use such animal for animal sacrifice.
(d) Nothing in this ordinance shall be construed to prohibit any person or establishment lawfully operating under the laws of this city and state from lawfully engaging in the slaughter or ritual slaughter of animals where the preparation or killing of such animals is primarily for food purposes.
(e) For the purpose of this section, the following words and phrases are defined as follows:
"Slaughter" means the killing of any animal for food purposes;
"Ritual slaughter" means the preparation and killing of any animal for food purposes in accordance with California Food and Agricultural Code Section 19501;
"Animal sacrifice" means the injuring or killing of any animal in any religious or cult ritual or as an offering to a deity, devil, demon or spirit, wherein the animal has not been injured or killed primarily for food purposes, regardless of whether all or any part of such animal is subsequently consumed.
This is impermissible under Church of Lukumi Babalu Aye v. City of Hialeah, since it expressly bans religious conduct precisely based on its religiosity. Lukumi also involved evidence that the city council was intentionally trying to go after a particular religion — Santeria — but that wasn't necessary to the analysis: If the statute on its face bans religious conduct based on its religiosity, it's presumptively unconstitutional, and even if that presumption can be rebutted in extraordinary cases, there's no reason to think that it would be here.
If the city had banned certain kinds of killings of animals without regard to the killings' religious nature, that wouldn't violate the Free Exercise Clause even if it ended up barring some religious rituals. But we're not dealing with such a religion-neutral ban here. (Whether applying such a religion-neutral ban to religious conduct would presumptively violate the California Constitution's religious freedom provision is still an open question in California.)
Kapparot is a custom in which the sins of a person are symbolically transferred to a fowl. It is practiced by some Jews shortly before Yom Kippur. First, selections from Isaiah 11:9, Psalms 107:10, 14, and 17-21, and Job 33:23-24 are recited; then a rooster (for a male) or a hen (for a female) is held above the person's head and swung in a circle three times, while the following is spoken: "This is my exchange, my substitute, my atonement; this rooster (or hen) shall go to its death, but I shall go to a good, long life, and to peace." The hope is that the fowl, which is then donated to the poor for food, will take on any misfortune that might otherwise occur to the one who has taken part in the ritual, in punishment for his or her sins.Apparently the fowl is at least sometimes slaughtered before being donated to the poor.
Thanks to Prof. Howard Friedman (Religion Clause) for the pointer.