Our Gemara on Amud Beis discusses that though sacrifices can be accepted as offerings from gentiles, they can only be fully burnt offerings but not shelamim. There is an interesting Midrash Tanchuma (Tzav 1–4) that records a dialogue between the gentile nations and Bilaam regarding sacrifices:

“Balaam the wicked was an advocate for the nations of the world. … We (gentiles) offer Him ten thousand times ten thousands rivers of oil. What did Abraham offer to Him? Was it not one ram? …but what did Abraham offer Him? His son. I might offer Him my son and daughter…See how crafty Balaam the wicked was! He began to say (in Numb. 23:4), ‘I have prepared the seven altars [and offered a ram and a bull on each altar].’ He did not say, ‘seven altars,’ but, ‘the [seven] altars.’ These are [all of the] seven altars, [which] they had built since the first Adam was created up to now. Now I am offering seven corresponding to the seven of them. ….”

“The Holy One, blessed be He, said to him, ‘O evil one, if I had desired an offering, I would have spoken to Michael and Gabriel, and they would have presented offerings to Me.’ …The Holy One, blessed be He, said to him, ‘What do you desire? To deceive yourself before Me? [To persuade] Me to accept offerings from the gentiles? You are not able. It is an oath (in the words of Lev. 24:8, cont.), “an everlasting covenant on the part of the Children of Israel.” It is a stipulation that I only accept offerings from Israel.’”

A shelamim is a sacrifice that is shared amongst the owner, God, and the kohanim. On a simple level, we can see that there is a certain intimacy in a shared meal, so to speak. This intimacy is reserved only for Jewish people, and therefore gentiles cannot bring that kind of sacrifice, but only a fully burnt offering, an olah.

The Midrash Tanchuma concludes:

“The peoples of the world said to Balaam, ‘Why did the Holy One, blessed be He, tell Israel to bring Him sacrifices without telling us anything?’ Balaam said to them, ‘The sacrifices are only peace (i.e., the peace offering). Whoever has accepted the Torah in which they are written must offer sacrifice. You rejected [Torah] from the start, and now you wish to offer sacrifices?’”

The Maharal (Gevuros Hashem 69) explains what sacrifices are and why gentiles are barred. He says it is the nature of the product to want to return back to where it came from. God sustains and created all. The sacrifice represents the voluntary return and joining of the person back to God through the process of the shelamim. Though nothing is ever truly separated from God, and therefore never really needs to return, and God does not really need “food,” Maharal offers a metaphor: The sea is always the sea. If you put a drop of water back in the sea, you will not have made much of an impression on the ocean. On the other hand, for the drop of water, it has authentically returned. So too, when man returns material existence to God.

So far is what the Maharal stated explicitly. Now I will add what I believe he said, with the disclaimer that it is my interpretation of his words: The other nations of the world do not have this particular affinity, and so long as they exist as gentile nations, they do not represent this form that can rejoin. This is where, like the angels, they are disqualified from sacrifices. Opposites are, in many respects, similar. Black is similar to white in that it is an absolute and there is no contrast. It would be just as difficult to see in a fully bright room as it is in a fully dark room. The angels cannot offer sacrifices because they are already too connected to God, and so it is meaningless to return. In the reverse sense, the gentiles are not connected enough to allow for this return, at least through the partnership process of shelamim. This is why, in the Midrash Tanchuma, God counters Bilaam with the response, “If I wanted your sacrifices, I could have taken them from the angels.”

Is this fair for the gentiles to be left out? It is not as exclusionary as it may seem at first glance. After all, they can convert and accept the Torah and generate this affinity. This may be why the Midrash concludes with the discussion about gentiles not being eligible because they rejected the Torah. This implies the opposite as well. If they would accept the Torah, they too can participate in the shelamim and reconnect with God.