Can a nonJew bring a sacrifice to the Bais Hamikdash

A nonJew is allowed to bring an Olah (a sacrifice that is completely burnt on the altar) as a free will offering in the same way that a Jew is allowed. The source for this is in Parshas Emor (22:18).

יח. דַּבֵּר אֶל אַהֲרֹן וְאֶל בָּנָיו וְאֶל כָּל בְּנֵי יִשְׂרָאֵל וְאָמַרְתָּ אֲלֵהֶם אִישׁ אִישׁ מִבֵּית יִשְׂרָאֵל וּמִן הַגֵּר בְּיִשְׂרָאֵל אֲשֶׁר יַקְרִיב קָרְבָּנוֹ לְכָל נִדְרֵיהֶם וּלְכָל נִדְבוֹתָם אֲשֶׁר יַקְרִיבוּ לַיהֹוָה לְעֹלָה:

 18. Speak to Aaron and to his sons and to all the children of Israel and say to them: Any man whatsoever from the house of Israel or from the strangers among Israel who offers up his sacrifice for any of their vows or for any of their donations that they may offer up to the Lord as a burnt offering

 As seen above, most translations speak of "Any man among Bnei Yisrael". However, Rabbi Sorotzkin in אזנים לתורה (Insights in the Torah) as well as the Malbim sets it up as

A man, a man of Bnei Yisroel, or a convert among Israel ...

 The descendants of Adam and Noach are called "Ish" (a man).  This means that anyone using his free will to acknowledge that Hashem is the Creator of the Universe is allowed to dedicate himself to Hashem. This is the symbolism of the Korbon Olah (burnt sacrifice). A nonJew is allowed to believe that Hashem has created various Powers (capital P deliberate) to run the world as his emissaries. This is the concept of Shituf (Shulchan Aruch, Orach Chaim 156, in the Rama). A Jew who makes this mistake would not be allowed to bring a korban. An example of this is the case of Eliyahu Hanavi on Mount Carmel. He calls on the Jews to make a decision and worship either Baal or Hashem, but not both. This is because the Jews are required to understand that everything in the Universe was created by Hashem and nothing exists as a separate power.

There is even the analogy of the difference between members of an empire. Those who live in the Imperial City under the direct rule of the Emperor would not be allowed to serve any of his subordinates. Since Hashem has taken us to himself and given us the Torah at Har Sinai, we can no longer be allowed to make the mistake that the rest of the world does.

An interesting point is the way that this division into three categories of human beings is set up.

1. Those who realize that there is a G0d who rules over everything, but think that the lesser powers still deserve service.

2. A "born" Jew who is restricted to the worship of Hashem because of Yestzias Mitzrayim (the Exodus) and the revelation at Sinai. We have been taken into the service of Hashem and commanded to become a "nation of Priests".

3. A righteous convert (ger) who has become a "naturalized citizen" and has raised himself to the level of a servant of Hashem. This person has explicitly taken the oath to only serve Hashem and is considered as if he had been at Sinai and received the Torah.

This also explains why this concept only applies to the Olah which is completely consumed on the altar. A nonJew cannot partake of the sacrifices, because only those who have been accepted into the service of Hashaem are allowed to "eat at Hashem's table". This also explains why a Jew who has abandoned his status is not allowed to bring a sacrifice even though a nonJew who has the same erroneous belief is allowed to do so.

Another point in Parshas Emor is that a Jew is only allowed to eat of a korban if he is tahor (ritually pure). Since a nonJew cannot become ritually pure, then he would never be able to partake of the korban, which means that he can never bring any korban other than an Olah. On the other hand, a ger has become tahor by immersing in the mikvah when he became a Jew.