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Gentiles were welcomed to bring their sacrificial offerings for G-d to the First and Second Temples in Jerusalem. They will participate even more at the Third Temple in the Messianic Era. This will happen especially during the festival of Sukkot, as prophesied in Zechariah:
“And it will come to pass that everyone left of the nations who came up against Jerusalem will go up from year to year to prostrate himself to the King, the L-rd of Hosts, and to celebrate the festival of Sukkot [Tabernacles]. And it shall be that whoever of all the families of the earth does not go up to Jerusalem to prostrate himself to the King, the L-rd of Hosts – upon them there shall be no rain.” (Zechariah 14:16-17)
The explanation in Metzudat David explains this future celebration of Sukkot by the Gentiles in the Messianic Era. It refers to their bringing offerings to be sacrificed at the Third Holy Temple.
In his explanation of the Torah section beginning with Genesis 12:1, Ramban (Nachmanides) wrote:
“Even in the time of Joshua… the Gentiles knew that this place was the most august of all. It was at the center of the inhabited world. [Torah] Tradition had taught them that it corresponds in this world to the celestial Temple where Divine Majesty… resides.”
When the First Temple was inaugurated by King Solomon, he beseeched G-d with an eloquent prayer. It included the following words in Kings I, 8:41-43. (These show that in the past, Gentiles were welcomed to the First and Second Temples. They will participate even more at the Third Temple.)
“If a foreigner who is not of Your people Israel comes from a distant land for the sake of Your Name – for they shall hear about Your great name and Your mighty hand and Your outstretched arm – when he comes to pray toward this House, oh, hear in Your heavenly abode and grant all [!] that the foreigner asks You for. Thus all the peoples of the earth will know Your name and revere You, as does Your people Israel. And they will recognize that Your Name is attached to this House that I have built.”
Torah Law holds that Gentiles are allowed to bring burnt offerings to G-d in the Temple when it is standing in Jerusalem. It is commanded (Leviticus 22:25) that an animal that is offered in the Temple by a Gentile must be unblemished. It must be unblemished to the same degree as an animal that is offered by a Jew. (For people who aren’t kohen priests, their offerings are sacrificed and offered by the Jewish priests in the Temple.)
The Prophet Isaiah foretold us about the even greater future participation of Gentiles. It will take place at the Third Temple (Isaiah 2:2-3):
“And it will come to pass at the end of days that the mountain of G-d’s House will be firmly established, even higher than the peaks, and all the peoples will flow toward it as a river. And many nations will go and will cry, ‘Let us go up toward the mountain of G-d’s House, to the House of the L-rd of Jacob, and we will learn from His ways and walk in His paths, for out of Zion goes forth Torah and the word of G-d from Jerusalem.’ “