How do those who reject both predestination and purgatory justify their beliefs?

Predestination

In John 4.34, Jesus said before He was crucified:

My meat is to do the will of him that sent me, and to finish his work. (John 4:34)

What is precisely the will of Him Who sent Jesus to live among us? The answer is in John 6:38-40:

I have come down from heaven, not to do my own will, but the will of the one who sent me. And this is the will of the one who sent me that I should not lose anything that he has given me, but should raise it to life on the last day. This is my Father’s will: That everyone who sees the Son and believes in him should have eternal life, and I will raise him to life on the last day.

In verse 44, we read how the Father chooses those He will give the Son – via His sovereignty in salvation:

No one can come to me unless the Father who sent me draws him, and I will raise him to life on the last day.

In John 17:1–2, we read that the Father gave the authority to the Son to judge all those the Father gave the Son:

After Jesus had said this, he looked up to heaven and said, Father, the hour has come. Glorify your Son, so that the Son may glorify you. For you have given him authority over all humanity so that he might give eternal life to all those you gave him.

The phrase “the hour has come” in the first verse above is a reminder of Jesus’ acceptance of the will of the Father for the Him to be crucified for our sins so that we may have eternal life. Jesus had the option to reject the will of the Father, for it is a dispositional or preferred will of the Father.

The above verses reveal a two-step process that leads to eternal life via the Father’s will for His Son. Firstly, the Father exercises His sovereignty to choose those He wants to have eternal life through His Son, and secondly, it is through the free will of those chosen to believe in His Son to have eternal life. So both God’s sovereignty in salvation and the free will of an individual determine whether the person will achieve eternal life.

Purgatory

There is a famous story in the Bible that clearly indicates that purgatory is not necessary for salvation. On Mount Calvary, one of the two thieves - sinners till the end of their lives - cried out to Jesus:

And he said unto Jesus, Lord, remember me when thou comest into thy kingdom. And Jesus said unto him, Verily I say unto thee, Today shalt thou be with me in paradise. (Luke 23: 42 – 43)

The Greek for “today” is σήμερον, sémeron, which according to Strong’s Concordance, also means “now”. Jesus answering in the affirmative implies He had had His Father’s confirmation of salvation for both of them at that instant, whilst they were still alive.

It is our complete faith in Christ that saves us, as per the exhortations of Paul the Apostle (Romans 10:8–10, New KJV):

But what does it say? “The word is near you, in your mouth and in your heart” (that is, the word of faith which we preach): that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved. For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation. (Romans 10:8–10)

It seems that there is an assumption here that unless God chooses who will go to heaven, then people must suffer for their own sins (in Purgatory). Nothing could be further from the truth in evangelical Christianity.

The Scriptures teach that God declares righteous those who have faith in Jesus--even the ungodly. In doing so, their sins are completely forgiven--past, present, and future. "Therefore, there is now no condemnation" for them. They have been sanctified (made holy), so there is no future purging or purification that they need to gain by their own suffering.

"But to the one who does not work, but believes in Him who justifies [declares righteous] the ungodly, his faith is credited as righteousness." Romans 4:5 NAS

This is the beauty of salvation, as Spurgeon discusses in his book, All of Grace. God takes an ungodly person and declares him righteous. Faith in Jesus is the channel through which righteousness is imparted to the ungodly one. The sinner is declared righteous--and righteous people have nothing to be purged of in Purgatory.

"Therefore there is now no condemnation for those who are in Christ Jesus. 2 For the law of the Spirit of life [a]in Christ Jesus has set you free from the law of sin and of death." Romans 8:1 NAS

There is no condemnation--none, zip, zero.

"For Christ also died for sins once for all, the just for the unjust, so that He might bring us to God, having been put to death in the flesh, but made alive in the spirit;" 1 Peter 3:18 NAS

Jesus died for sons once for all--not once and then there needs to be more suffering by us later, but once for all.

"For as through the one man’s disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous." Romans 5:19 NAS

It was the one act of righteousness performed by Jesus Christ that results in righteousness to those who trust in Jesus--it has nothing to do with our own works of righteousness, which merit nothing in God's sight.

So, the evangelical perspective which denies Purgatory and denies Predestination justifies the position by the doctrine of salvation itself. God offers salvation/justification (the declaration of righteousness) to all people who put their trust in Jesus. God does not require us to suffer for our own sins in Purgatory, because Jesus already suffered for them once for all. This salvation is available to "whosoever will."

There is still a binary choice, but it's not God who makes the decision. He leaves it to each of us to choose for ourselves one way or the other, and gives us our whole lifetime to make that decision. God could make the decision for us — He has that power — and He knows in advance — if concepts like "in advance" even have any meaning for a being that exists outside of time — what choice each of us will make. After all, He made us. What He desires is for each of us to choose Him of our own will. It is not interesting to Him if the choice is forced upon us.

There is an interesting philosophical question here of whether there is really any difference at all between determining an outcome and merely knowing an outcome with absolute certainty, when those outcomes are produced by a system that one designed, set in motion, and directs for oneself, as God does with us and our environment. God gives us something akin to free will, but is it really free will as we know it if He made each of us in the first place, knows what our choices will be in any situation, and has absolute power over all situations? This is especially interesting when you look at psychology studies that show how human behavior is much more about programmed responses and brain chemicals than any of us want to acknowledge.

For this reason, I don't really find the question of predestination vs free choice very interesting... I tend to think of it as two sides of the same coin. Do we have free choice? Yes! You can say we do. Are we predestined? You can say that as well, and not be entirely wrong about it. This question has historically caused a huge split in Christiandom, but I ultimately see it as more about philosophy than theology. Your answer has implications for how your view soteriology, but either way you still look to Jesus. Does it really matter how you view soteriology as long as you're looking at the right source? I think also that Jesus would find the question uninteresting... at least in a relative sense. He is far more concerned that look at Him as Lord, and with how you treat your fellow man.