Grace

Judas was chosen to be an apostle by Jesus for a purpose, specifically to betray Him.

Jesus knew from the beginning who they were that believed not, and who should betray him... Have not I chosen you twelve, and one of you is a devil? He spake of Judas Iscariot the son of Simon: for he it was that should betray him, being one of the twelve.
     (John 6:64,70-71)

Judas had a mission, and was chosen for that mission. He was told to do it, even commanded. Read carefully, did the Lord really command Judas to betray Him?

When Jesus had thus said, he was troubled in spirit, and testified, and said, Verily, verily, I say unto you, that one of you shall betray me.
Then the disciples looked one on another, doubting of whom he spake.
Now there was leaning on Jesus' bosom one of his disciples, whom Jesus loved.
Simon Peter therefore beckoned to him, that he should ask who it should be of whom he spake.
He then lying on Jesus' breast saith unto him, Lord, who is it?
Jesus answered, He it is, to whom I shall give a sop, when I have dipped it. And when he had dipped the sop, he gave it to Judas Iscariot, the son of Simon.
And after the sop Satan entered into him. Then said Jesus unto him, That thou doest, do quickly.
Now no man at the table knew for what intent he spake this unto him.
For some of them thought, because Judas had the bag, that Jesus had said unto him, Buy those things that we have need of against the feast; or, that he should give something to the poor.
He then having received the sop went immediately out: and it was night.
Therefore, when he was gone out, Jesus said, Now is the Son of man glorified, and God is glorified in him. (John 13:21-31)

Jesus specifically told Judas to do it, quickly, and he did. He did all that he was told to do. He was chosen for this moment. The other eleven apostles didn't know what it meant, but Judas did.

I don’t understand, why was he chosen to do a heinous crime? Why was he told to do it?  There was purpose, so Jesus could fulfill His mission. Is Judas Iscariot a hero, or a villain? Should we condemn or exalt him? For, without his courageous mission to betray the Lord, we could not be saved. Peter is replaceable; we would still be saved without Paul or John, but Judas was a necessary part of the plan. Without him the Savior would not have finished His work.

The Jews
Likewise, without the Jews willingness to take upon themselves the blood of the Son of God, we would be left without salvation. The counsel of the Jews was told by the High Priest (the prophet) that Jesus needed to die for them, to save their nation, to gather all of Israel, and for the world, that salvation may come to all. They needed to put Him to death.

Then gathered the chief priests and the Pharisees a council, and said, What do we? for this man doeth many miracles.
If we let him thus alone, all men will believe on him: and the Romans shall come and take away both our place and nation.
And one of them, named Caiaphas, being the high priest that same year, said unto them, Ye know nothing at all, Nor consider that it is expedient for us, that one man should die for the people, and that the whole nation perish not.
And this spake he not of himself: but being high priest that year, he prophesied that Jesus should die for that nation; And not for that nation only, but that also he should gather together in one the children of God that were scattered abroad.
Then from that day forth they took counsel together for to put him to death.
(John 11:47-53)

The Jews were commanded by the High Priest to kill Jesus. It was their mission to slay the Passover Lamb. They knew He was sent from God, as confessed by Nicodemus:

There was a man of the Pharisees, named Nicodemus, a ruler of the Jews: The same came to Jesus by night, and said unto him, Rabbi, we know that thou art a teacher come from God: for no man can do these miracles that thou doest, except God be with him.
(John 3:1-2)

Judas, and the Jews needed to perform this act so that the prophecy could be fulfilled, and the world could be saved. They did as they were commanded to do. In that sense, they allow us to be saved because Jesus had to die.

Wherefore, as I said unto you, it must needs be expedient that Christ—for in the last night the angel spake unto me that this should be his name—should come among the Jews, among those who are the more wicked part of the world; and they shall crucify him—for thus it behooveth our God, and there is none other nation on earth that would crucify their God.  (2 Nephi 10:3)

What does “Behoove” mean?

Behoove: to be necessary or proper for, as for moral or ethical considerations; be incumbent on.  (Google Dictionary)

It was planned. The Jews had to fulfill their mission to crucify their God. Nobody else in the world would do it. Nobody else could do it. It was set up to happen this way. It was “necessary and proper.” Those people were specifically sent to Earth to that place and time to do what they did. For centuries priests had symbolically sacrificed the clean, white, unbroken lamb at Passover, now it was time for them to do the real thing. The law was fulfilled in them, ending animal sacrifice. He is the last sacrifice, and the Jews were chosen to perform it.

Woe unto the world because of offences! for it must needs be that offences come; but woe to that man by whom the offence cometh!  (Matthew 18:7)

Those who make offences are necessary for the Father's plan to be carried-out. If the Jews had worshiped Him and refused to betray and kill the Son of God, there would be no salvation for the world. The Pharisees, Caiaphas, Pontius Pilate, and Judas Iscariot had important roles to play, extremely important. In fact, they were central to the Father’s plan, even more so than Peter, James, John, and Paul. Their role was essential for Jesus Christ to become the Savior of the world. In that sense, we owe a debt of gratitude to them. If they had not done their part, we would not have the option of salvation. They fulfilled their mission in life, and because they did we’re all saved. In that sense, we could be more grateful to them than we are to those who wrote about them in the Bible.

Repentance and Grace
I don’t understand. Some are called to greatness, others to infamy. Why? Why did the Lord choose Judas to be infamous? Did Judas ask for the job? I don’t like the idea. He wasn’t chosen for salvation, but we’re all saved because of what he did. Thus, there must be another way to look at the situation. Perhaps Judas is just the same before God as Peter. Peter denied knowing Him, lying, and abandoning Him during His darkest hour,

And Peter remembered the word of Jesus, which said unto him, Before the cock crow, thou shalt deny me thrice. And he went out, and wept bitterly.  (Matthew 26:75)

Judas, after realizing what He did, went back to repent, confessing that he had done wrong,

Saying, I have sinned in that I have betrayed the innocent blood. And they said, What is that to us? see thou to that.
And he cast down the pieces of silver in the temple, and departed, and went and hanged himself.  (Matthew 27:4-5)

Judas was finished with his mission as Peter was just starting his. Both are repentant. Judas is loved as much as Peter. Both are offered the same grace.

To give a modern contrast, Mother Theresa is offered the same grace as Hitler, and both have access to the same forgiveness. Perhaps, those who sin more, such as Judas or Hitler, are more grateful for the grace of Christ, as Jesus explained to Simon, the Pharisee.

There was a certain creditor which had two debtors: the one owed five hundred pence, and the other fifty. And when they had nothing to pay, he frankly forgave them both. Tell me therefore, which of them will love him most?
Simon answered and said, I suppose that he, to whom he forgave most. And he said unto him, Thou hast rightly judged.  (Luke 7:41-43)

If he repents, perhaps Hitler will love God more than Mother Theresa, if she repents. Hitler fulfilled prophecy in persecuting the Jews, who took upon themselves the responsibility of crucifying their God. In front of Pontius Pilate the Jews said,

His blood be on us, and on our children.
(Matthew 27:25)

And, indeed they did, as prophesied long before. God told them He would judge them, and afflict them.

...the judgments of the Father upon my people who are of the house of Israel, verily, verily, I say unto you, that after all this, and I have caused my people who are of the house of Israel to be smitten, and to be afflicted, and to be slain, and to be cast out from among them, and to become hated by them, and to become a hiss and a byword among them...  (3 Nephi 16:9) 

And I have trampled them in my fury, and I did tread upon them in mine anger, and their blood have I sprinkled upon my garments, and stained all my raiment; for this was the day of vengeance which was in my heart.  (D&C 133:51)

The Lord says, "I have caused..." and "I have trampled..." He caused them to be smitten. Hitler was doing His will. They indeed became “a hiss and a byword” in the world, describing well the philosophy and actions of the Third Reich. Hitler did as he was instructed, fulfilling his mission -- and prophecy.

Often, those we consider to be the worst sinners are fulfilling prophecy, and doing the will of the Lord. They are part of the plan from the beginning.

But, grace is for all, even the "worst" of us. One verse of a hymn describes the situation of Judas, and the Jews, perfectly:

No creature is so lowly,
No sinner so depraved,
But feels thy presence holy
And thru thy love is saved.
Tho craven friends betray thee,
They feel thy love’s embrace;
The very foes who slay thee
Have access to thy grace.

        (O Savior Thou Who Wearest, by Karen Lynn Davidson, b. 1943. © 1985 IRI)

The fact remains that we are all offenders, and fall short of salvation. We all need the grace of God. Jesus offers His grace equally to all.

We’re all in the same boat.
We’re all offenders
We’ve all crucified our Lord.
We’ve all sinned.
None are acceptable before God.
We’re all enemies to God.

In terms of grace, the worst sinner is exactly the same as the greatest prophet. Those who betrayed Him, and killed Him, will stand before Him exactly the same as those who were His friends. All are offered the same grace - complete forgiveness. “The prisoners shall go free!” The grand design includes all. None are left out. No matter who we are, no matter what we’ve done doesn’t matter; the grace of the Lord, Jesus Christ is offered to all.

...and he inviteth them all to come unto him and partake of his goodness; and he denieth none that come unto him, black and white, bond and free, male and female; and he remembereth the heathen; and all are alike unto God, both Jew and Gentile.  (2 Nephi 26:33)

This is literally true! All are alike to God. It doesn’t matter who I am, or what I’ve done. It doesn’t matter if I’m black or white. It doesn’t matter if I’ve committed heinous crimes or bounteous charity. It doesn’t matter if I’m ignorant or lettered, we are all the same in the eyes of God! Peter had a vision that explained this concept to him.  The Lord said:

What God hath cleansed, that call not thou common.  (Acts 10:15)

Subsequent events lead Peter to understand what the Lord meant:

Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons:  (Acts 10:34)

We are all His children. He loves us all with an Eternal love, and offers every one all He has. Nobody is left out; no matter who we are, or what we’ve done, we’re the same. God offers His love, forgiveness, and grace to everyone!