I'm not sure how you can see the bible saying things that are opposite and not in harmony with each other.
And I, am not sure how someone spiritual (1 Corinthians 2:13 KJV) can look at Acts 10:35 KJV and Titus 3:5 KJV and claim they are saying the same thing. They clearly aren't. Perhaps your problem is a natural one (1 Corinthians 2:14 KJV).
Did Cornelius earn acceptance?
Actually, yes! Look at why his prayers and alms came up for a memorial before God (Acts 10:3-4 KJV). It was because of this:
Acts 10:1 There was a certain man in Caesarea called Cornelius, a centurion of the band called the Italian band,
Acts 10:2
A devout man, and one that feared God with all his house, which gave much alms to the people, and prayed to God alway.
Cornelius was a blesser and received a blessing because of it!
Genesis 12:3
And I will bless them that bless thee, and curse him that curseth thee: and in thee shall all families of the earth be blessed.
This will also be true for Gentiles who bless Israel during the tribulation. Their blessing will be to inherit the kingdom prepared for you from the foundation of the world. Those who don't bless Israel shall go away into everlasting punishment
Matthew 25:31
When the Son of man shall come in his glory, and all the holy angels with him, then shall he sit upon the throne of his glory:
Matthew 25:32
And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth his sheep from the goats:
Matthew 25:33 And he shall set the sheep on his right hand, but the goats on the left.
Matthew 25:34 Then shall the King say unto them on his right hand,
Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
Matthew 25:35 For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in:
Matthew 25:36 Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me.
Matthew 25:37 Then shall the righteous answer him, saying, Lord, when saw we thee an hungred, and fed thee? or thirsty, and gave thee drink?
Matthew 25:38 When saw we thee a stranger, and took thee in? or naked, and clothed thee?
Matthew 25:39 Or when saw we thee sick, or in prison, and came unto thee?
Matthew 25:40 And the King shall answer and say unto them,
Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me.
Matthew 25:41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
Matthew 25:42 For I was an hungred, and ye gave me no meat: I was thirsty, and ye gave me no drink:
Matthew 25:43 I was a stranger, and ye took me not in: naked, and ye clothed me not: sick, and in prison, and ye visited me not.
Matthew 25:44 Then shall they also answer him, saying, Lord, when saw we thee an hungred, or athirst, or a stranger, or naked, or sick, or in prison, and did not minister unto thee?
Matthew 25:45 Then shall he answer them, saying, Verily I say unto you, Inasmuch as ye did it not to one of the least of these, ye did it not to me.
Matthew 25:46 And these shall go away into everlasting punishment: but the righteous into life eternal.
That's not going to happen for anyone today! There are no blessings unless you are in Christ!
Ephesians 1:3 Blessed be the God and Father of our Lord Jesus Christ,
who hath blessed us with all spiritual blessings in heavenly places in Christ:
There's only way for anyone today to be in Christ and that's "by the gospel"!
Ephesians 3:6 That the Gentiles should be fellowheirs, and of the same body, and partakers of his promise
in Christ by the gospel: