"No one gets to the Father except through the Son."
An interesting rendering. Forgive me for saying this, but it makes Jesus sound like the Father's bodyguard.
But I agree with what you cite from Scripture:
No man cometh unto the Father, but by me (John 14:6)
In fact, the Lord goes into great detail as to how exactly He will determine who will come unto the Father and who will not (Matthew 25:32-46):
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: And He shall set the sheep on his right hand, but the goats on the left.
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: 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: Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto Me.'
Then shall the righteous answer him, saying, 'Lord, when saw we Thee an hungred, and fed thee? or thirsty, and gave Thee drink? When saw we Thee a stranger, and took Thee in? or naked, and clothed Thee? Or when saw we Thee sick, or in prison, and came unto Thee?'
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.'
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: For I was an hungred, and ye gave Me no meat: I was thirsty, and ye gave Me no drink: 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.'
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?'
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.'
And these shall go away into everlasting punishment: but the righteous into life eternal.
He also makes clear that much more will be expected of Christians than of non-Christians:
And that servant, which knew his lord’s will, and prepared not himself, neither did according to his will, shall be beaten with many stripes. But he that knew not, and did commit things worthy of stripes, shall be beaten with few stripes. For unto whomsoever much is given, of him shall be much required: and to whom men have committed much, of him they will ask the more (Luke 12:47-48)
For, as He says,
Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven (Matthew 7:21).