Answer:This man is used by many as an example of a so-called "Gentile" non-Israelite being saved. The place of birth, or citizenship tells us nothing about race. But this man's race can be determined by Scripture, even if he is not described as a "Jew" [or "Judean"]. In the AV of Acts 10:28, Cornelius is described as being of another nation but, the Greek text uses the word allophulos which is a compound of allos [another of the same kind], and phulos [a kindred tribe (phule)].
Cornelius was a devout man, we are told, and he feared [the] God, therefore he was one who could believe. According to Vine, devout means careful as to the presence and claims of God. So Cornelius knew the Old Testament claims of God upon Israel. We do not find devout being used of people other than Israelites. Also, he feared "God" [Acts 10:2] and he prayed to [the] God and was heard by [the] God. "God" here is ho theos, the term used to denote the one true God. So, Cornelius was not a Roman polytheist! He was an Israelite!
The evidence that Cornelius was not an Israelite is given by the people of Israel. "Now the apostles and brethren who were in Judea heard that the Gentiles had also received the word of God. And when Peter came up to Jerusalem, those of the circumcision contended with him, saying, "You went in to uncircumcised men and ate with them!"" (Acts 11:1-3). By declaring that Cornelius and his household were uncircumcised, the Jewish Christians were stating that Cornelius was not under the covenant of Moses. Paul talks of this in Ephesians 2:11-12, "Therefore remember that you, once Gentiles in the flesh -- who are called Uncircumcision by what is called the Circumcision made in the flesh by hands -- that at that time you were without Christ, being aliens from the commonwealth of Israel and strangers from the covenants of promise, having no hope and without God in the world." Being uncircumcised in the flesh was equivalent to be a Gentile.
In Acts 10:28, Peter tells Cornelius, "You know how unlawful it is for a Jewish man to keep company with or go to one of another nation." You argued that the Greek word, alophulos refers to people of the same nationality, but born in a foreign location. Quoting from The Complete Biblical Library Greek-English Dictionary, "This word is formed from two Greek words: allos, 'different, other,' and phule, 'a tribe, people, race, or nation.' It means one of alien descent, a foreigner. It was used in this sense in classical Greek culture, as well as by the Jews. In the Septuagint it is the word used for "Philistines' in such passages as I Samuel 13:3, Psalm 108:9, and Isaiah 2:6. In Isaiah 61:5 it denotes 'aliens.' ... In the New Testament allophulos is found only in Acts 10:28 to denote the Gentiles." Thayer's Greek Lexicon states, "when used in Hellenistic Greek in opposition to a Jew, it signifies a Gentile [A.V. one of another nation]."
You stated that devout is only applied to Israelites. "But the Jews stirred up the devout and prominent women and the chief men of the city, raised up persecution against Paul and Barnabas, and expelled them from their region" (Acts 13:50). Hence in Antioch of Pisidia there were women among the Gentiles who were described as being devout.