A righteous man is saved. Acts 10:22
It appears that you are unable to connect the dots.
If that were true, and from the introduction of Cornelius at the beginning of Acts, then yes he would have been saved.
However, when Peter explained to the believing Jews in ch 11 as to WHY he went to the home of Gentiles, he said this:
11:14 - He will bring you a message through which you and all your household will be saved.’
So, just who is the "He" here? Glad you asked.
11 “Right then three men who had been sent to me from Caesarea stopped at the house where I was staying.
12 The Spirit told me to have no hesitation about going with them. These six brothers also went with me, and we entered the man’s house.
13 He told us how he had seen an angel appear in his house and say, ‘Send to Joppa for Simon who is called Peter.
Oh, so it was the Holy Spirit who told Peter to go there. And then in v.13 we have Peter basically quoting Cornelius stating what the angel told him.
So your argument is against an angel of God, who was sent to Cornelius with instructions. And Cornelius told Peter the angel told him that he WOULD BE SAVED by Peter's message. (v.14)
Why are you being so stubborn against the truth?
And they said, Cornelius the centurion, a just man, and one that feareth God, and of good report among all the nation of the Jews, was warned from God by an holy angel to send for thee into his house, and to hear words of thee.
Yeah, he was religious and acknowledged the existence of God and sought Him. That has saved exactly NO ONE EVER.
It was the specific gospel message brought by Peter that Cornelius believed and was saved.