Question: "Why were non-Israelites allowed to participate in the sacrificial system?"
Answer: Non-Israelites were not to participate in many areas of the Jewish sacrificial system. However, one way in which a foreigner could participate was in the burnt offering (Leviticus 17:8–9). The foreigner was to bring his burnt offering to the tabernacle, just like any natural-born Israelite. When a burnt offering was made at the tabernacle, it was clear that the sacrifice was made to the Lord Almighty and not to another god.
In addition, Numbers 15:14-16 says, “For the generations to come, whenever a foreigner or anyone else living among you presents a food offering as an aroma pleasing to the Lord, they must do exactly as you do. The community is to have the same rules for you and for the foreigner residing among you; this is a lasting ordinance for the generations to come. You and the foreigner shall be the same before the Lord: The same laws and regulations will apply both to you and to the foreigner residing among you.” Many traditions were restricted only to Jews, but those that were not could be observed by Gentile sojourners living among the people of Israel.
The Feast of Weeks and the Feast of Booths/Tabernacles were also mentioned as festivals that a “sojourner” could attend (Deuteronomy 16). Sojourners were to be treated well, since the Israelites had likewise been sojourners in Egypt (Exodus 23:9).
While many distinctions were made in the Old Testament between Jewish and non-Jewish practices, the Old Testament is clear that God’s love extends to all who will trust in Him. A striking example is found in the book of Jonah. Jonah, a prophet, runs from God after being called to preach against the wickedness of the Gentile city of Nineveh. After God gets His prophet back on track, Jonah preaches to the people of Nineveh. They fast in repentance, and God has mercy on them and spares their city. Through it all, Jonah learns what Peter learns centuries later: “How true it is that God does not show favoritism but accepts from every nation the one who fears him and does what is right” (Acts 10:34–35).