They’ve been doing this since before the time of Jesus.
No
“The practice of kapparot is mentioned for the first time by Amram ben Sheshna of Sura Academy in Babylonia in 670 and later by Natronai ben Hilai, also of Sura Academy, in 853. According to Joshua Trachtenberg, the rite probably originated toward the end of the Talmudic period.“ Kapparot - Wikipedia https://en.wikipedia.org/wiki/Kapparot
The only permitted sacrifice was at the tabernacle. Kapparot is an inovation made possible by kabalah and the destruction of the temple.
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