No, most Christians have correctly understood Paul that Gentiles are not obligated to keep Moses. But as for Romans 3:31, let's put this verse back into context. In the following passage, Paul eventually will switch his definition of "Law". At first, however, he is talking about the Law of Moses or what the Jews call the Torah. Notice how the passage reads if we substitute the word "Torah" in place of "Law."
Originally Posted by episkopos
21 But now apart from the Torah a righteousness of God has been manifested, being witnessed by the Torah and the Prophets*, 22 even a righteousness of God through faith in Jesus Christ for all those who believe; for there is no distinction; 23 for all have sinned and fall short of the glory of God, 24 being justified as a gift by His grace through the redemption which is in Christ Jesus; 25 whom God displayed publicly as a propitiation in His blood through faith. [This was] to demonstrate His righteousness, because in the forbearance of God He passed over the sins previously committed; 26 for the demonstration, [I say], of His righteousness at the present time, so that He would be just and the justifier of the one who has faith in Jesus. 27 Where then is boasting? It is excluded. By what kind of Torah? Of works? No, but by a Torah of faith**. 28 For we maintain that a man is justified by faith apart from works of the Torah. 29 Or is God [the God] of Jews only? Is He not [the God] of Gentiles also? Yes, of Gentiles also, 30 since indeed God who will justify the circumcised by faith and the uncircumcised through faith is one. 31 Do we then nullify the Law through faith? May it never be! On the contrary, we establish the Torah.
* Taken together the phrase "The Torah and the Prophets" refer to the entire Old Testament, which also include "The Writings."
** Here Paul begins to talk about a "Torah of faith". He draws a distinction between the "Torah of works" and the "Torah of faith", which is the Torah he and the other apostles established.
The contrast is between those who are seeking to be justified through the works of the law, rather than seeking to be justified through faith. He claims that God is granting justification outside the Jewish context of keeping the Torah of works, granting justification according to a new Torah of faith, which is not really new since he will eventually point out that Abraham lived according to such a Torah of faith and did not find justification in a Torah of works.