For Christian Gentiles, Shavuot, which commemorates the giving of the Torah at Sinai to Israel, is completely irrelevant. While Christians have mixed feelings about how they should relate to Israel, they are unanimously against the idea that the Torah of Moses should be binding as a Way of Life and be the only framework for informing our Worldview.
Messianic Gentiles, however, tend to feel conflicted about Shavuot, as they hear conflicting messages within the Messianic Movement about how Gentiles should relate to Torah. First Fruits of Zion teaches that Gentiles are excluded from the Covenant People of Israel and not required to keep the Torah of Moses and therefore Gentiles have an ambiguous identity:
"[The Acts 15 decision] left open questions about observance and intergenerational continuity. By not requiring Gentiles to take on the legal status of Jews, the apostles created a new category, so to speak. Neither Jew nor proselyte, the Gentile believer was left with an ambiguous and tenuous status among the people of God that can best be described as that of a God-fearer: a monotheist non-Jew worshipping in a Jewish context,” Boaz Michael, D. Thomas Lancaster, “ ‘One Law’ and the Messianic Gentile”, Messiah Journal 101.Today, I'd like to point to an enlightening Midrash containing in Sifre Deuteronomy. It offers a story in which G-d offered the Torah to all of mankind before finally deciding to give the Torah just to Israel. It's enlightening because of the REASONS that Gentile mankind offered for rejecting the Torah. Each time G-d offered the Torah, Gentiles rejected it because acceptance would've meant forfeiting Gentile-ness (and becoming indistinguishable from Israel):
A. Another teaching concerning the phrase, 'He said, 'The LORD came from Sinai':
B. When the Omnipresent appeared to give the Torah to Israel, it was not to Israel alone that he revealed himself but to every nation.
C. First of all he came to the children of Esau. He said to them, 'Will you accept the Torah?'
D. They said to him, 'What is written in it?'
E. He said to them, 'You shall not murder' (Exod. 20:13)
F. They said to him, 'The very being of 'those men'...and of their father is to murder, for it is said, 'But the hands are the hands of Esau' (Gen. 27:22). 'By your sword you shall live' (Gen. 27:40).'
G. So he went to the children of Ammon and Moab and said to them 'Will you accept the Torah?'
H. They said to him, 'What is written in it?'
I. He said to them, 'You shall not commit adultery' (Exod. 20:13).'
J. They said to him, 'The very essence of fornication belongs to them...for it is said, 'Thus were both the daughters of Lot with child by their father' (Gen. 19:36).'
K. So he went to the children of Ishmael and said to them, 'Will you accept the Torah?'
L. They said to him, 'What is written in it?'
M. He said to them, 'You shall not steal' (Exod. 20:13)
N. They said to him, 'The very essence of their...father is thievery, as it is said, 'And he shall be a wild ass of a man,' (Gen. 16:12).'
O. And so it went. He went to every nation, asking them, 'Will you accept the Torah?'
P. For so it is said, 'All the kings of the earth shall give you thanks, O LORD, for they have heard the words of your mouth' (Ps. 138:4).
Q. Might one suppose that they listened and accepted the Torah?
R. Scripture says, 'And I will execute vengeance in anger and fury upon the nations, because they did not listen' (Mic. 5:14).
S. And it is not enough for them that they did not listen, but even the seven religious duties that the children of Noah indeed accepted upon themselves they could not uphold before breaking them.
T. When the Holy One, blessed be he, saw that that is how things were, he gave them to Israel."
One day Gentiles will stop being Gentiles as they destroy their "idols" and go to Jerusalem to learn the Torah. Why? Because those who G-d calls will make a decision to answer His call rather than making up excuses, "I cannot accept because acceptance would mean that I must change my identity." But they will say, "I will hear and do everything you say even if it means forfeiting my Gentile identity, my idolatry, my ancestral laws; I will join your People and follow your Torah."