> “Is anyone ever denied adoption who genuinely seeks it?”
> “Does that then mean that the works of seeking to be ‘adopted’ are the real deciding factor?”
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That is all answered definitively in John 6:
[37] All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out.
[39] And this is the Father’s will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day.
[40] And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day.
44] No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.
As you can see, works have absolutely nothing to do with it. It was the Father that drew you to the son.
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This is a classic if / then statement:
If I cometh to Him I will no wise be cast out. What happens if I don't?
If I seeth the Son, and believeth on Him, I will be raised up. What happens if I don't see or believe?
How is a requirement for me to "cometh, seeth and believeth" not an obligation upon me to perform works to achieve Salvation?