Even if Paul's primary focus is to counter the Judaizers, it does not undermine the Reformed position. The person with whom you're discussing is oversimplifying Paul's letter to the Romans.
"A. Romans is the most systematic and logical doctrinal book of the Apostle Paul. It was affected by circumstances in Rome, therefore, it is an occasional document. Something occurred that caused Paul to write the letter. However, it is the most neutral of Pauls writings, in that Pauls way of dealing with the problem (possibly the jealousy between believing Jewish and Gentile leadership) was a clear presentation of the gospel and its implications for daily life.
B. Pauls presentation of the gospel in Romans has impacted the churchs life in every age:
1. Augustine was converted in A.D. 386 reading Romans 13:1314.
2. Martin Luthers understanding of salvation was radically changed in A.D. 1513 as he compared Ps. 31:1 to Rom. 1:17 (cf. Hab. 2:4).
3. John Wesley was converted in A.D. 1738 by hearing Luthers sermon on the introduction to Romans.
C. To know Romans is to know Christianity! The letter shapes the life and teachings of Jesus into bedrock truths for the Church of all ages.
PURPOSE
A. An appeal for help for his missionary trip to Spain. Paul saw his apostolic work in the eastern Mediterranean finished (cf. 16:2023).
B. To address the problem in the Roman church between believing Jews and believing Gentiles. This was probably a result of the expulsion of all Jews from Rome and their later return. By then the Jewish Christian leaders had been replaced by Gentile Christian leaders.
C. To introduce himself to the Roman church. There was much opposition to Paul from sincere converted Jews in Jerusalem (Jerusalem Council of Acts 15), from insincere Jews (Judaizers in Galatians and II Cor. 3, 1013), and from Gentiles (Colossians, Ephesians) who tried to merge the gospel with their pet theories or philosophies.
D. Paul was accused of being a dangerous innovator, adding recklessly to Jesus teaching. The book of Romans was his way of systematically defending himself by showing how his gospel was true, using the Old Testament and the teachings of Jesus (the Gospels)."
Utley, R. J. (1998). Vol. Volume 5: The Gospel according to Paul: Romans. Study Guide Commentary Series. Marshall, Texas: Bible Lessons International.
It is clear, at least to me, there are multi-purposes in Paul's letter to the Romans, and might I suggest the primary purpose is found in Chapter 1:1-18.
Romans 1:1 Paul, a bondservant of Jesus Christ, called to be an apostle, separated to the gospel of God 2 which He promised before through His prophets in the Holy Scriptures, 3 concerning His Son Jesus Christ our Lord, who was born of the seed of David according to the flesh, 4 and declared to be the Son of God with power according to the Spirit of holiness, by the resurrection from the dead. 5 Through Him we have received grace and apostleship for obedience to the faith among all nations for His name, 6 among whom you also are the called of Jesus Christ;
7 To all who are in Rome, beloved of God, called to be saints:
Grace to you and peace from God our Father and the Lord Jesus Christ.
8 First, I thank my God through Jesus Christ for you all, that your faith is spoken of throughout the whole world. 9 For God is my witness, whom I serve with my spirit in the gospel of His Son, that without ceasing I make mention of you always in my prayers, 10 making request if, by some means, now at last I may find a way in the will of God to come to you. 11 For I long to see you, that I may impart to you some spiritual gift, so that you may be established 12 that is, that I may be encouraged together with you by the mutual faith both of you and me.
13 Now I do not want you to be unaware, brethren, that I often planned to come to you (but was hindered until now), that I might have some fruit among you also, just as among the other Gentiles. 14 I am a debtor both to Greeks and to barbarians, both to wise and to unwise. 15 So, as much as is in me, I am ready to preach the gospel to you who are in Rome also.
16 For I am not ashamed of the gospel of Christ, for it is the power of God to salvation for everyone who believes, for the Jew first and also for the Greek. 17 For in it the righteousness of God is revealed from faith to faith; as it is written, The just shall live by faith.
The New King James Version. 1982 (Ro 1:117). Nashville: Thomas Nelson.
Notice the text in bold? To all (in Rome) called to be Saints, indicates the intended audience of the letter is Christians in Rome (and all Christians by way of implication and application), not unconverted unregenerate non-Christian Judaizers. I believe verses 1:15-17 indicate the primary purpose, and set the theme for the rest of the book.