I think the problem is the blending of verses (and writers) to make John 3:16 say what is not stated.
God loved the world by sending His only (unique) begotten (of the same essence, i.e., equal to God) Son (representing a father) that whoever believes (anybody without exception) will have everlasting life.
It is a simple statement that does not go against Calvinism (the whoever part) or free-will theology.
I think this is super simple and is being made different degrees of complex depending on the teacher.
God has one son by a woman. This Son is Jesus Christ and this word "begotten" is to be understood in the same way that this word is used elsewhere in the scriptures. God is the father and Mary is the mother. Jesus has the Divine nature from his father and he is a natural man through his mother. He is the only man who has ever been born in this fashion. Therefore he is the "only" begotten son of God.
This is a fundamental of the faith. If this is not believed and accepted a person is not saved. The entire gospel of John was written for the expressed reason to make this perfectly clear and is required of all men in that day as to what they must believe to have eternal life.
I am not guessing about this. John actually gave this reason for writing his gospel.
John 20:30 And many other signs truly did Jesus in the presence of his disciples, which are not written in this book:
31 But these are written, that ye might believe that
Jesus is the Christ, the Son of God; and that believing ye might have life through his name.
In the context of this gospel and the person of Jesus Christ from his introduction to Israel by John the Baptist it is required that the Jews believe that Jesus Christ is the Messiah of Israel and the Son of God. Nothing else is required at this point and this is not required of any other race.Those who will have eternal life will believe this and be justified. They are not required to believe in his death, burial, and resurrection. It is required they believe he is the Son of God and the Messiah of Israel who was promised in their OT scriptures. This is not a essage that will justify a gentile.
Mat 10:5 These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not:
6 But go rather to the lost sheep of the house of Israel.
7 And as ye go, preach, saying, The kingdom of heaven is at hand.
8 Heal the sick, cleanse the lepers, raise the dead, cast out devils: freely ye have received, freely give.
9 Provide neither gold, nor silver, nor brass in your purses,
10 Nor scrip for your journey, neither two coats, neither shoes, nor yet staves: for the workman is worthy of his meat.
11 And into whatsoever city or town ye shall enter, enquire who in it is worthy; and there abide till ye go thence.
12 And when ye come into an house, salute it.
13 And if the house be worthy, let your peace come upon it: but if it be not worthy, let your peace return to you.
14 And whosoever shall not receive you, nor hear your words, when ye depart out of that house or city, shake off the dust of your feet.
15 Verily I say unto you, It shall be more tolerable for the land of Sodom and Gomorrha in the day of judgment, than for that city.
Lk 10:1 After these things the Lord appointed other seventy also, and sent them two and two before his face into every city and place, whither he himself would come.
2 Therefore said he unto them, The harvest truly is great, but the labourers are few: pray ye therefore the Lord of the harvest, that he would send forth labourers into his harvest.
3 Go your ways: behold, I send you forth as lambs among wolves.
4 Carry neither purse, nor scrip, nor shoes: and salute no man by the way.
5 And into whatsoever house ye enter, first say, Peace be to this house.
6 And if the son of peace be there, your peace shall rest upon it: if not, it shall turn to you again.
7 And in the same house remain, eating and drinking such things as they give: for the labourer is worthy of his hire. Go not from house to house.
8 And into whatsoever city ye enter, and they receive you, eat such things as are set before you:
9 And heal the sick that are therein, and say unto them, The kingdom of God is come nigh unto you.
10 But into whatsoever city ye enter, and they receive you not, go your ways out into the streets of the same, and say,
11 Even the very dust of your city, which cleaveth on us, we do wipe off against you: notwithstanding be ye sure of this, that the kingdom of God is come nigh unto you.
12 But I say unto you, that it shall be more tolerable in that day for Sodom, than for that city.
Matt 15:21 Then Jesus went thence, and departed into the coasts of Tyre and Sidon.
22 And, behold, a woman of Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, thou son of David; my daughter is grievously vexed with a devil.
23 But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us.
24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
25 Then came she and worshipped him, saying, Lord, help me.
26 But he answered and said, It is not meet to take the children's bread, and to cast it to dogs.
27 And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters' table.
28 Then Jesus answered and said unto her, O woman, great is thy faith: be it unto thee even as thou wilt. And her daughter was made whole from that very hour.
What preaching will save the gentiles?
Jn 12:20 And there were
certain Greeks among them that came up to worship at the feast:
21 The same came therefore to Philip, which was of Bethsaida of Galilee, and desired him, saying, Sir, we would see Jesus.
22 Philip cometh and telleth Andrew: and again Andrew and Philip tell Jesus.
23 And Jesus answered them, saying, The hour is come, that the Son of man should be glorified.
24 Verily, verily, I say unto you, Except a corn of wheat fall into the ground and die, it abideth alone: but if it die, it bringeth forth much fruit.
25 He that loveth his life shall lose it; and he that hateth his life in this world shall keep it unto life eternal.
26 If any man serve me, let him follow me; and where I am, there shall also my servant be: if any man serve me, him will my Father honour.
27 Now is my soul troubled; and what shall I say? Father, save me from this hour: but for this cause came I unto this hour.
28 Father, glorify thy name. Then came there a voice from heaven, saying, I have both glorified it, and will glorify it again.
29 The people therefore, that stood by, and heard it, said that it thundered: others said, An angel spake to him.
30 Jesus answered and said, This voice came not because of me, but for your sakes.
31 Now is the judgment of this world: now shall the prince of this world be cast out.
32 And I, if I be lifted up from the earth, will draw all men unto me.
33 This he said, signifying what death he should die.
34 The people answered him, We have heard out of the law that Christ abideth for ever: and how sayest thou, The Son of man must be lifted up? who is this Son of man?
35 Then Jesus said unto them, Yet a little while is the light with you. Walk while ye have the light, lest darkness come upon you: for he that walketh in darkness knoweth not whither he goeth.
36 While ye have light, believe in the light, that ye may be the children of light. These things spake Jesus, and departed, and did hide himself from them.
37 But though he had done so many miracles before them, yet they believed not on him:
If one will understand the scriptures he must accept and note the transitions in the scriptures. Every person on the earth has a duty to believe God to be justified, but only that which God says to them. If the woman of Canaan or the Greeks at the feast had believed what Israel was required to believe while Jesus ministered on the earth they would not be justified and God did not say they would be.
Read the scriptures believing the words is my best advice to Christians.