That is not the best example because Cornelius already feared God and prayed to him. Maybe he was a pagan at one point in his life, or maybe his parents believed in the God of Israel. We don't know. There were four types of people in the ancient world, Israelites called 'Jews' in the first century (in translation at least). Then there were proselytes, men who had been circumcised who took on them the obligation to keep the law of Moses along with women in their households. Another category were pagans. Then there were God-fearing Gentiles who believed in the God of Israel who went to the synagogue, maybe outside of a partition that separated them from the Jews and proselytes. Some of the Pharisees tried to get Gentiles to convert through circumcision. Apparently, this practice influenced some of the churches and Paul opposed it.
It is improbable that Cornelius being a Roman soldier should fall into any of the types of people you have mentioned. A critical look at Acts 10 shows he is none. ----- starting from Peter's trance, his utterances and the attitude of the Jews when they heard he went to see the gentiles.
The truth is that, as Peter said, in every nation (and of course religion), he that fears God and works righteously is accepted of God.
What matters in our service of him is the sincerity and integrity of heart in which we follow him. God searches the heart and he is no respecter of persons or any show of religiosity. He accepts all who call upon his name and worship him in sincerity and truth and then guides them to salvation irrespective of religion or race. The story of Cornelius brings this to light.
There are many Cornelius out there who are non Christians , who are faithfully and sincerely following and serving the living God. And God knows them all.