So, in your mind, there are sinners who are born again, and have a heart that seeks God, but are not Christians?
My view is that by God's providence, all who are born again come to trust in the "seed" (Messiah) sent by God as their savior/redeemer. Note, the classic Reformed ordo salutis is 1) election, 2) predestination, 3) gospel call 4) inward call 5) regeneration, 6) conversion (faith & repentance), 7) justification, 8) sanctification, and 9) glorification. (Rom 8:29-30)
Where specifically does John 3 say such a ridiiculous thing?
Jhn 3:1 Now there was a man of the Pharisees, named Nicodemus, a ruler of the Jews;
Jhn 3:2 this man came to Jesus by night and said to Him, "Rabbi, we know that You have come from God {as} a teacher; for no one can do these signs that You do unless God is with him."
Jhn 3:3 Jesus answered and said to him, "Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God."
Jhn 3:4 Nicodemus *said to Him, "How can a man be born when he is old? He cannot enter a second time into his mother's womb and be born, can he?"
Jhn 3:5 Jesus answered, "Truly, truly, I say to you, unless one is born of water and the Spirit he cannot enter into the kingdom of God.
Jhn 3:6 "That which is born of the flesh is flesh, and that which is born of the Spirit is spirit.
Jhn 3:7 "Do not be amazed that I said to you, 'You must be born again.'
Jhn 3:8 "The wind blows where it wishes and you hear the sound of it, but do not know where it comes from and where it is going; so is everyone who is born of the Spirit."
Note that "Nick at Night" came to Jesus to gain revelation from a prophet, maybe he was seeking what he had to do to gain eternal life. Instead of giving special "secret knowledge" or some method to attain heaven, Yeshua says something totally unexpected. Instead of telling Nick what he can do, Yeshua says what the Holy Spirit must do! He says that it's up to the choice of the Spirit to decide if, when, and how v8. Salvation is of God, not of man, lest any man should boast. The book of John, especially chapters 3, 6, 10 is a powerful testimony of the providence of God in salvation.