Rambam explains in Mishneh Torah that Noahides are forbidden to "observe" Jewish holy days (Biblical festivals) in the manner of the Jews (i.e. stopping from certain actions in a similar manner to the observance of the Jewish Sabbath).
From Laws of Kings 10:9 - The general principle governing these matters is: Gentiles are not allowed to innovate religious practices for themselves, including taking commandments upon themselves based on their own decisions. They should observe their own part of the Torah [the Noahide Code] without adding or subtracting any Divine commandments.
From Laws of Kings 10:10 - A Noahide who wishes to do one of the commandments that will bring with it some tangible benefit is allowed to do so, for the purpose of receiving that benefit [for one's self or for the society].
An example of a Jewish commandment with no tangible benefit for Noahides: making a point to specifically eat matzah on the night when Jews are commanded to observe the Passover seder meal.
Examples of Jewish commandments that do have tangible benefits for Noahides: returning a lost object to its owner, giving proper charity, honoring parents, .
Laws of Kings 10:9 teaches that Noahides are permitted to "delve deeply" into Torah study if it involves study of the commandments and principles in the Noahide Code. On the other hand, studying the Hebrew Bible and the explanations of any Torah commandments is permitted for Noahides, if it is not done as in-depth study. So for example, on the night of Passover, Noahides may read and/or discuss the Torah passages about the Exodus from Egypt and/or about the Jewish commandments associated with Passover.
See: a) Forum thread on "Noahide Torah Study":
https://asknoah.org/forum/showthread.php?tid=13
b) Part I, ch. 5, in "The Divine Code," Vol. 1, by Rabbi Moshe Weiner:
https://asknoah.org/books/the-divine-code
Nevertheless, it is far from the truth to imagine that faithful Noahides are in some sort of "limbo" between false religions and Judaism, just because they should not observe the commandments of the Jewish Biblical festivals. First of all, a Torah-faithful Noahide has connected and established his lot with the One True G-d, the G-d of Israel; he is living a life of spiritual truth in fulfilling what G-d desires from him, and with this he earns the merit of eternal reward in the World To Come.
Furthermore, there are some of the Jewish festivals that Noahides have more of a connection to, and they can honor these as special days (for example, with prayers and selected Torah reading). For example:
- Rosh Hashanah, the annual Day of Judgment for all people;
- Sukkot, the annual time of judgment for the rainfall that each nation will receive, which is also characterized by the themes of unity and joy;
- Displaying the candles of Hanukkah to public view (without making a blessing), which is a practical way of accomplishing the good deed of reminding people of G-d’s miracles in the world.
Further information:
Special days for Noahides:
https://asknoah.org/essay/noahide-holidays
Special days (audio):
https://asknoah.org/audio/holidays-for-noahides
Rosh Hashanah:
Insights:
https://asknoah.org/insights?cat=194
Audio:
https://asknoah.org/audio/rosh-hashanah-the-new-year
Sukkot:
https://asknoah.org/audio/messages-from-sukkot
https://asknoah.org/essay/connection-bet...d-a-sukkah
https://asknoah.org/faq/noahides-at-the-third-temple
Hanukkah:
https://asknoah.org/essay/what-is-hanukah
https://asknoah.org/essay/sharing-hanukkah-joy