Whatever, God clearly says, through Peter, that He does not wish for one to perish, but all to come to repentance.
If he predestined those who would be saved, then His desires and His actions are at odds with each other.
4His_Glory -- Eve is not said to have been responsible for the entrance of sin into the world because she was deceived. I would think, and maybe I am wrong, that the same would apply to many who believe Calvinism to be true. They are deceived. The teachers, however, may find themselves in a very uncomfortable position when face to face with Christ.
In the meantime, you seem to refer to 'doctrines of grace' as though that were somehow exclusive to Calvinism. Hardly. I am saved by grace. God's grace. And I am most assuredly not a Calvinist!
It is also a severe error in logic to presume that because believers are predestined to be conformed to the image of Christ that certain people are then predestined to become believers. There is no connection at all there. It is like saying that the winning team in the Olympics is predestined to stand on the tallest podium and that that 'predestination' also means that one certain team will have to win. Saying what will happen to the winners does not determine WHO the winners will be.
Same with salvation. Those who believe are predestined to be conformed to the image of Christ through the agency and power of the Holy Spirit. But who the believers are is not a matter of predestination. Foreknowledge, yes. Predestination, no.
God leaves NO man to himself when it comes to repenting and believing, but presents every man alive with enough truth to either follow or reject (Romans 1). It is up to each man to follow that truth or suppress it. No one is forced or created to do either. Those who follow what truth God has presented them with will be led by Him to Christ Jesus, who will turn none away. Calvinists go for the second half of that and completely ignore the first part, which is a major theme of Paul's writings. Half a gospel is not the gospel at all, really, but a perversion of it.
To answer your question, not everyone who hears believes because they have a choice in the matter. We can bless God with our submission or curse Him with our independent rebellion. The choice is ENTIRELY ours.
The work is completely done by Him, but the choice to accept or reject is ours.
A person separated from God may not have any spiritual understanding, but he does have spiritual thirst. And that is all that is necessary.
And yes, I do understand Calvinism. For several years I was the head deaf interpreter for Sproul here on the west coast. It was his material that got me studying the Bible intensely, looking for the truth of this matter.