For Noahides to understand the Noahide laws effectively and to understand what is the ideal and right way to take as a non-Jew not converted, it is necessary for him to study more than just the list of obligations. If he has the intent to learn about the Noahide laws deeper (than just the surface literal understanding) and to learn the proper path for someone like himself, then the studying of all parts of the Oral Torah should be made permissible for him. This makes it possible for him to effectively act on Torah that relates to him and his world. Arguments as follows.
Understanding what a law actually is. Interpreting by פשט alone is dangerous. Exegesis at all four levels is needed for the Noahide to properly understand the law and subsequently carry out. Exegesis is learned from the Oral Torah and also found there are answers to simple questions like “what is a mitzvah?”. This would give the Noahide the right context to interpret their laws and obligations correctly.
Understanding God - Knowing God. How does His providence work, how can man have a relationship with Him, etc. - This is explained by all parts of the Oral Torah. Knowledge of HaShem is important for the Noahide to have because it will influence his behavior his decisions, etc. For example, is not Shabbat intricately connected with God’s creation of this world? And is not the creation of this world intricately connected with God Himself?
Learning the Hebrew language with intent to clarify Noahide laws and proper gentile path. Without the Oral Law the Noahide would fail to obtain a precise understanding of what the text is trying to convey because of the lack of Nikud.
Jewish ideology, that is, ideal and true ideology; and understanding righteousness. Having the proper intent–to best fulfill gentile obligations and to make choices driven by moral guidance–the Noahide should have access to study all parts of the Oral Torah, so that he has knowledge of the proper way and so that he can for example model his behavior after holy men. Surely proper gentile culture is not secular.
The Noahide has the obligation to pray to God. But without study of the Oral Torah he is left wanting. Given he has the proper intent–to learn say about tefillin or about Jewish rituals or even about esoterical practices knowing that these are applied by Jews only (though the Rambam held [in Mishneh Torah] that gentiles can do many Jewish practices out of curiosity or as an optional mitzvah) and learn about such topics to know more about God and how prayer is conducted by His chosen people–his study of the Oral Torah would help him in this obligation.
Proper intimacy. All parts of the Oral Torah give detail on this. Being barred from having forbidden sexual relations is not enough. But proper intimate practices should also be known by the Noahide, so that he doesn’t follow the ways of immorality and being suffering to the world.
Establishment of laws and courts of justice. Surely these courts should not be secular. For a gentile judge to know how to properly rule over a court and how to form it, it is necessary to study Jewish best practices exhibited in their bet din and being derived from the Oral Torah. It is important for judges to avoid making judgements that are abhorrent to God and to judge in a way that settles the world yishuv olam.
How to fight the evil inclination. Limiting gentile Torah study to a leaflet of a few laws and their descriptions is not as effective as studying the depths of the Oral Torah and the critical advice therein brought by the holy Jewish sages.
In our times, Noahides generally lack a strong community with the right morals, and so they should be given the (s)word–the Torah in its full breadth–given they have the proper intention (as discussed above), to protect themselves and their communities.