Question: "If the Jewish people do not offer animal sacrifices, how do they believe they can receive forgiveness from God?"
Answer: For the most part, the Jewish practice of animal sacrifice to receive forgiveness stopped in the year A.D. 70 when the Roman army destroyed the Holy Temple in Jerusalem, the place where sacrifices were offered. The practice was briefly resumed during the Jewish War of A.D. 132-135, but was ended permanently after that war was lost. There were also a few communities that continued sacrifices for a while after that time.
Essentially, Jews stopped offering sacrifices because they didn't have a proper place to offer them. The Torah (the Law of Moses) specifically commanded Israel not to offer sacrifices wherever they felt like it. They were only permitted to offer sacrifices in the one place that God has chosen for that purpose (see Deuteronomy 12:13-14).
Today, modern Jews believe that forgiveness for sins is obtained through repentance, prayer and good deeds. They use verses like the one found in Hosea 6:6 which says, “For I delight in loyalty rather than sacrifice, And in the knowledge of God rather than burnt offerings.”
But both the Old and New Testaments are very clear: “For the life of the flesh is in the blood, and I have given it to you on the altar to make atonement for your souls; for it is the blood by reason of the life that makes atonement” (Leviticus 17:11). And also, “All things are cleansed with blood, and without shedding of blood there is no forgiveness” (Hebrews 9:22).
Jesus Christ, the Jewish Messiah, was offered up as the once-for-all sacrifice for sin. Less than a generation later, the Jewish temple was destroyed because the need for animal sacrifices no longer existed. Animal sacrifices were merely a “type” of the perfect Sacrifice—the Lamb of God who takes away the sins of the world. The sacrifice of Christ paid the debt for the sins of mankind, both Jew and Gentile.