Answer
Animal sacrifice continued in the Jewish community even after the time of Christ. When the Jewish temple was destroyed and the nation of Israel extinguished in AD 70, Jewish animal sacrifice on a broad scale ceased to be a unified national practice. It could not be continued properly according to Mosaic Law because of its association with the temple.
The Christian community never practiced animal sacrifice on the whole, though some Jewish Christians did participate in non-atoning Jewish sacrifices prior to AD 70 (see Acts 21:26). Christians did not participate in sacrifices because Jesus' sacrifice perpetually satisfies the requirements of the Law in this regard (Heb. 10:12).
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.