They think if God exercises justice on a person, damning them eternally, without giving them "a chance" to vote themselves into heaven in their own ability, then he's a monster, unjust, unfair, the author of evil, not God &c &c &c. It just goes to show they have no fear of accusing God of anything, or, they don't know him, or, they are doing so in ignorance.
How is man accountable to God if he does not make the decision to receive or reject Christ? How is man responsible for his own fate in this?
It seems to me that the scenario that you present means that God arbitrarily chooses some people out for salvation; and by default, certain people out for condemnation.
Now the Bible teaches that God is just; but the god that you present to us is not just: and therefore he must not be the God of the Bible.
The God of the Bible gives everyone a fair opportunity to receive or reject the author of their salvation.
Everyone has access to the witness of creation around them to the eternal power and Godhead of the Lord (Romans 1). If they obey that light and believe in the Lord God, they will receive the 2nd light (conscience, Romans 2). If they receive that light, understanding that they are sinners, they will be faced with the third light, the light of Christ and the Cross. If they receive the 3rd light, they will be saved.
Each perspective receiving of light is a choice and a decision on the part of the person who is faced with the light in front of them.
Therefore every man is responsible for his own fate when he shall stand before the Lord. If he ends up being cast into the lake of fire, he will have no one but himself to blame.