Christians believe that Jesus died for their sins and God needed that to happen because there must be a sacrifice to the sin and it just can't be removed as that will make God unjust, also they claim that it's the same thing with Allah(swt) in Islam based on the hadith of (Sahih Muslim 2767), as it's mentioned that Allah(swt) will put the sin of Muslims on the disbelievers(in this case Jews and Christians) so they ask If their sin can just go away, then why does it have to go on the disbelievers? Why can’t the sin just be obliterated? Why can’t the sin just be placed aside in Hell itself away from everyone?
Their interpretation of the hadith is wrong, as the burden of sin can not be transferred and it is actually unjust to punish someone for the deeds of another.
لا تكسب كل نفس إلا عليها ولا تزر وازرة وزر أخرى
Every soul earns not [blame] except against itself, and no bearer of burdens will bear the burden of another.
What the hadith actually means is that the sins of the Muslims would be forgiven while those of the Jews\Christians would be retained. They will receive punishment because of their own Kufr and misdeeds, not on behalf of the sins of the Muslims.
See Fath al-Bari etc.
Perhaps a passage from Gil Eaton's Islam and the Destiny of Man may help throw light on your question:
For Christians, nothing less than the sacrificial death of the God-man Jesus could redeem Adam's sin and restore the cosmic balance disturbed by that sin.
In the Islamic version of the Fall, Adam was forgiven and his son blotted out, so that it counted for nothing (although, it's consequences were not, as such, abolished; Adam was not restored to Paradise).
In the Muslim view, what was required of Jesus, as also of Muhammed, was not an act of universal redemption but simply the repetition, in a form appropriate to those later times, of the age old message given to Adam, and man's sin is therefore primarily one of forgetfulness. If we were not by nature so forgetful, and if we were not so readily inclined to idolatry (preferring illusions to reality), there would not have been any need for either.
This is why it is said that Islam is neither more nor less than a restoration of the primodorial religion of mankind, 'the perennial philosophy.'
'He hath ordained for you that religion He enjoined upon Noah, and which We have revealed into thee, and which We enjoined upon Abraham and Moses and Jesus, so you should make firm the religion and not be divided therein' (Q.42:13)
This religion, this wisdom, is as much a part of the total human situation as the winds and the tides and the earth itself. A man has two eyes, two ears and so on; and unless his heart is sick, he has - as a man - this God-given wisdom, which is a part not merely of his heritage but of his nature. Even in those who seem most ignorant, most une lightened, the pilot-light still burns; but for this, they would not qualify as human beings.
One interesting gloss here is that a famous (or infamous) European philosopher, Heidegger, who originally began training for the Lutheran ministry but finding that this was not his vocation, took up philosophy instead, introduced a new term into philosophy - alethia, or un-forgetfulness from lethe, which means forgetfulness and this, to my mind, recalls Islams emphasis on man's forgetfulness. Again, like many philosophers, he hasn't credited where he took up this term; so it's impossible to say whether or not he borrowed the term from Islam; but in any case, it is not a far-fetched supposition ...
And Allah knows best.
On «Redemption by the Cross»
The Hebrew name Yeshu'a (Latin and English: Jesus) means "salvation" or "redemption". The teaching that Jesus ﷺ redeemed is based not least on this name. In connection with the image of the sacrificial lamb, the atonement for the Jewish Pessach, this thought became the Christian central tenet "Jesus redeemed us through his death on the cross". It is first formulated in the letter of his first scholar, Peter:
1 Peter 1:18-19
You know that you were ransomed from the futile ways inherited from your fathers, not with perishable things such as silver or gold, but with the precious blood of Christ, like that of a lamb without blemish or spot.
Later in Christian tradition, this was shortened, distorting the meaning, to the statement that the believers (i.e. Christians) had been redeemed through the cross, they spoke of the "Holy Cross".
What the cross really was
The cross is not holy at all, it has been an awful torture instrument. Knowing this, Jesus has prayed
Gospel of Matthew 26:37
And taking with him Peter and the two sons of Zeb'edee, he began to be sorrowful and troubled. Then he said to them, "My soul is very sorrowful, even to death; remain here, and watch with me." And going a little farther he fell on his face and prayed, "My Father, if it be possible, let this cup pass from me; nevertheless, not as I will, but as thou wilt."
Salvation through Jesus
Reading the teachings of Jesus in the Gospels, it does not initially sound like salvation at all:
Gospel of Matthew 5:43-45,48
You have heard that it was said, `You shall love your neighbor and hate your enemy.' But I say to you, Love your enemies and pray for those who persecute you, so that you may be sons of your Father who is in heaven; for he makes his sun rise on the evil and on the good, and sends rain on the just and on the unjust. (...) You, therefore, must be perfect, as your heavenly Father is perfect.
Gospel of Matthew 10:23-25
And Jesus looked around and said to his disciples, "How hard it will be for those who have riches to enter the kingdom of God!" And the disciples were amazed at his words. But Jesus said to them again, "Children, how hard it is to enter the kingdom of God! It is easier for a camel to go through the eye of a needle than for a rich man to enter the kingdom of God." And they were exceedingly astonished, and said to him, "Then who can be saved?"
He sets the bar unreachably high, the prophet whose name means “Redeemer”. Doesn't he know that no one can do that? He knows it. The following verse is
Gospel of Matthew 10:26
Jesus looked at them and said, "With men it is impossible, but not with God; for all things are possible with God."
There is no «automatic» salvation just because of ones religion
The Holy Quran, AlMa'ida 5:18
The Jews and the Christians say, “We are the children of God, and His beloved.” Say, “Why then does He punish you for your sins?” In fact, you are humans from among those He created. He forgives whom He wills, and He punishes whom He wills. To God belongs the dominion of the heavens and the earth and what lies between them, and to Him is the return.
The Prophet John (a.s.) said to his fellow Jews
Gospel of Matthew 3,8-9
Bear fruit that befits repentance, and do not presume to say to yourselves, ‹We have Abraham as our father›; for I tell you, God is able from these stones to raise up children to Abraham.
Jesus ﷺ in the Gospel of Matthew 7:21-23
Not every one who says to me, 'Lord, Lord,' shall enter the kingdom of heaven, but he who does the will of my Father who is in heaven. On that day many will say to me, `Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?' And then will I declare to them, 'I never knew you; depart from me, you evildoers.'
Alike, the Quran says that there is no salvation coming just from saying «we are the children of God». Faith and deeds are linked. Many more than than the three passages cited below state that the reward is to those who believe and do good deeds:
The Holy Quran, Al-Baqara 2:277
Those who believe, and do good deeds, and pray regularly, and give charity—they will have their reward with their Lord; they will have no fear, nor shall they grieve.
The Holy Quran, Maryam 19:96
Those who believe and do righteous deeds, the Most Merciful will give them love.
The Holy Quran, Yunus 10:9
As for those who believe and do good deeds, their Lord guides them in their faith. Rivers will flow beneath them in the Gardens of Bliss.
There is no blanket salvation of anyone. Jesus did not die for the sins of people coming after him - in fact he did not die at all because God saved him - but he had to go through torture and suffered because God lead him this way.
The Core of Salvation
The salvation is that we don't have to be perfect because we can't be perfect, that we can fail because we must fail, and that we can forgive just as we are in need of forgiveness. Tho one who cannot fail will fail. Or he blames others, which makes his own sin even bigger. Those who cannot forgive hold themselves captive and others with them.
But that, too, is salvation: that we are not satisfied with what is innate to us, but are allowed to try to grow beyond that and try the impossible without fear of failure. Just as a plant grows towards the sun without ever coming close to it, this teaching of God shows us a direction, shows us a way, and although the goal is also closer than the sun, reaching this goal is nevertheless not the goal, but that Growth of our soul and our society, the intensification of life in the moment, in our lifetime and beyond - in order to ultimately increase what makes us heavenly according to our strength.
The Source of Salvation
You may read the Word of God as it came onto us from Jesus ﷺ or from Muhammad ﷺ: Salvation comes from God to whomever tries his best to follow His Word:
The Holy Quran, An-Nisa 4:26-28
God intends to make things clear to you, and to guide you in the ways of those before you, and to redeem you. God is Most Knowing, Most Wise. God intends to redeem you, but those who follow their desires want you to turn away utterly. God intends to lighten your burden, for the human being was created weak.