The plain and simple answer: YES! Once they accept the God of Abraham, Isaac and Jacob, they are no longer considered “Gentiles”; they are “Hebrews” – which, in Hebrew, means “to cross over.” They can still call themselves “Christians” if they choose, but the fact remains, once you accept YHWH, you MUST obey His “forever” commands.
Many are under the erroneous impression that Torah is “just for the Jews,” but that can’t be true, because Torah consists of God’s Divine Instructions in Righteousness, without which we would have NO blueprint for moral, holy living.
Simply “believing in Jesus” doesn’t cut it because “belief” requires “action.” What does our worship of YHWH (most likely pronounced Yah-way) consist of if we don’t bother with His Divine Rules for holy/set apart living?
Still, many (if not most) attempt to wriggle out of obedience to YHWH’s “forever” commands (i.e., the Seventh Day Sabbath and the Feasts/Mo’edim) because the concept of Torah is simply too foreign. It’s all “Old Testament” to them, which they’ve been told doesn’t pertain to Christians. (Never mind that believers in Jesus are “one in Messiah” (Galatians 3:28-29, John 17:21) and are therefore, bound to the same rules.)
They therefore attempt to twist passages such as Acts 15 into meaning that Christians only need to adhere to certain Torah rules. This is simply not true because, for instance, Numbers 15:13-16 tells us four times in a row that ALL who accept Him are to do exactly as His people do.
And HIS people have always been Torah observant!
Speaking of Acts 15, it is imperative to remember that Acts 15 is referring to man-made laws and not the Torah itself! Yet, the "million dollar question" that has successfully split the Messianic Faith today is: Are Gentiles required to obey Torah?
The answer, of course, is a resounding, "YES!"
Why? Well, let’s allow Scripture to explain itself:
Acts 15:19. Because of this (I) say that you should not be those oppressors who from the Gentiles are turning to Elohim. 20. But we will send (word) to them that they should abstain from uncleanness of sacrifices (idols) and from adultery and from things that are strangled and from blood. 21. For from ancient generations in all cities Moshe had preachers in the synagogues that on every Shabbat they read him.” (AENT)
Note verse 19 which, in plainer language, says: "It is my opinion is that we should not put obstacles in the way of the Goyim who are turning to God!” In other words, Acts 15 plainly states that the expectation of the non-Jewish converts was that they would learn Moshe (Torah) as they grew in their relationship with Mashiyach and his people.
Read in context, Acts 15:20-21 shows there is one Torah for Israel and the Gentile who dwells with her - yet, many try to use it as "proof" that Christians don't have to keep Torah. That is because they don't realize that Acts 15 is referring to man-made laws and not the Torah itself....
Footnotes from the AENT concerning this issue:
 That which is "sacrificed" unto other gods according to YHWH's Word in D'varim/Deuteronomy 32:17 is sacrificed unto devils. Vayikra/Leviticus 17:12-16 commands that Jew and Ger (foreigner) NOT eat blood, or any animals that die of themselves. The prohibition against fornication is wide spectrum, against all manner of physical perversion and spiritual whoredom. These Torah directives are eternally binding on all who follow Y'shua Mashiyach and who seek the Malchut (Kingdom) of Elohim.
 It's a very clear fulfillment of Isaiah 56:1-9. Gentile converts are observing Shabbat and learning Torah as one body along with Jews. Shortly thereafter, Marcion, whom Polycarp referred to as "the firstborn of the devil" built the first all-Gentile church to promote Christo-Paganism. Marcion held his services on Sunday which blended with Zeus (the sun god) culture and projected a hybrid Je-Zeus identity in opposition to the Jewish Mashiyach.
The modern theologies of "Jesus Christ" are based more on Hellenism than on original fundamental Hebraic values. Marcion coined the words "Old - New Testament" and did his very best to warn Gentiles away from Torah and "the God of the Old Testament." Marcion invented theologies known as replacement, dispensational, supercessionism, etc., which are very popular among Christianity today.
Yes - Read in context Acts 15 plainly states that the expectation of the non-Jewish converts was that they would learn Torah as they grew in their relationship with Mashiyach and his people. What a beautiful thing for those who know they are “one in Messiah!”