When discussing the concept of different obligations to the Torah for different groups of people, there is a common misconception that Jewish people are obligated to all of the 613 commandments.
The reality is that no one is obligated to all 613 commandments. For example, a man is not obligated to all the mitzvot that women are, and women are not obligated to all the mitzvot that men are. Levites have different mitzvot than the regular Israelite, priests have different mitzvot than Levites, and the high priest has still more unique mitzvot; but alas, it is not the full 613. But is there a way where we can all connect with each of the 613 mitzvot even if not every one is directly incumbent upon us?
Recently I have been reading a book on Exodus by Rabbi Sholom Brodt. In one section he directly addresses this question:
Reb Tzvi Elemielech of Dinov, in his sefer Derech Mitzvotecha, explains that each mitzvah is ideally performed on all three levels: thought, speech, and action. On the levels of thought and speech, each one of the Torah’s 613 mitzvot was given equally to every single Jew. It is only on the level of action that we are not all equally commanded. For example, although women are not commanded to put on tefillin, they are connected to the mitzvah in thought and speech. Likewise, a man who never takes on the vow of a nazir is still connected to this mitzvah through learning about it and probing all its details. Although I am not a kohen and thus will not actually perform all the sacrificial rituals, I become involved with all these mitzvot by studying them in thought and speech and considering their practical implications in my service of G-d. Each mitzvah is deeply significant and teaches us how to be close with HaShem in different ways. 
According to the approach offered here, every Jew can connect with all 613 of the mitzvot on at least two of the three levels, that of thought and speech. When they study a mitzvah that is not incumbent upon them and discuss its implications, they are connecting to the commandment.
In Messianic Judaism I think we can apply this same principle to Gentiles disciples of Yeshua. While Gentiles in Messiah have a number of Torah commandments that are incumbent upon them, they have fewer than any other group.  However, that does not mean that they can’t connect to all 613 mitzvot. One the one hand Rabbi Brodt says “On the levels of thought and speech, each one of the Torah’s 613 mitzvot was given equally to every single Jew” and Paul says that “The Jews were entrusted with the oracles of God [i.e., the Torah]” (Romans 3:2). But on the other hand, the Apostle Paul also tells us that Gentiles in Messiah were at one time “separated from [Messiah], alienated from the commonwealth of Israel and strangers to the covenants of promise, having no hope and without God in the world. But now in [Messiah Yeshua] you who once were far off have been brought near by the blood of [Messiah]” (Ephesians 2:12-13). While the Torah was originally given to the Jewish people, part of being brought near to the “covenants of promise” is being brought near to the Torah.
With that said, when Gentiles in Messiah study and speak of Torah laws that they are not obligated to, they can still connect with them in thought and speech. In turn, when any Jewish or Gentile follower of Yeshua reads and studies the Torah, even things to which they are not obligated, they are connecting with the whole of the 613 commandments on a very deep level where the entire Torah becomes a part of their very being. We are then conforming into the image of Messiah Yeshua, who was the living Torah.
- Rabbi Sholom Brodt, Exodus: The Model of Personal Liberation (Jerusalem, Israel: Yeshivat Simchat Shlomo, 2013).
- For a full discussion of a Gentile's obligation to the Torah see Toby Janicki, God-Fearers: Gentiles and the God of Israel (Marshfield, MO: First Fruits of Zion, 2012).