Islamic Eschatology – Day of Judgment, Paradise & Hell Fire
The Quran distinguishes for us between a non-Muslim who has faith in God and a non-Muslim who is a kaafir (disbeliever) and teaches that while former may have a chance to gain Allah's forgiveness and mercy on Judgment Day, the latter will not be able to escape His punishment.
Disclaimer - Please note that this writing is discussing the non-Muslims situation strictly from a theological perspective i.e. their spiritual relationship with Allah, and not legal perspective of Islamic Law. As per Islamic law all non-Muslims legal status is kaafir i.e. legally speaking they do not believe in Islam and are considered outside of the religion. The legal status of a person is important to ascertain because of consequences of such legal standing with regard to marriage, birth, death, property inheritance etc. As per Islamic law a non-Muslim does not inherit from Muslims, nor do Muslims inherit from non-Muslims. Moreover, a non-Muslim is not buried according to Islamic funeral rites, nor is he or she prayed for after death by Muslims. A non-Muslim cannot marry a Muslim neither can a Muslim marry a non-Muslim, generally speaking. This is to be noted before moving on to our subject of Judgment day.
There seems to be no consensus among Islamic scholars in regards as to what will exactly happen to all non-Muslims on the Judgment Day, who were good and righteous in this world. That is because Judgment in the Hereafter is a decision making process that belongs only to Allah ﷻ, we cannot really pass any judgments for all or some non-Muslims in this world. It would be ignorance for Muslims to pass a judgment for all non-Muslims that is only reserved for the Hereafter. However, due to the fact that Quran’s message is universal and encompasses entire humanity, we notice that some ayahs of the Quran do give hope to the non-Muslims of gaining Allah’s forgiveness and immense mercy. Now there are non-Muslims who live and die as kaafir or disbelievers and that is a separate matter. First we need to understand the matter of non-Muslims i.e. those who have not accept Islam but do have their own faith in God and live according to it.
For instance, non-Muslims such as Christians, believe in One God and His existence but also assign divine qualities to Jesus son of Mary (alaihi salaam) and believe in his divinity. The Quran mentions an Ayah that gives hope to the good among them of Allah’s Mercy on Judgment day despite the fact of their breach of His Oneness: (Al Quran 4:171–173) People of the Book (i.e. Christians), do not go to excess in your religion, and do not say anything about God except the truth: the Messiah, Jesus, son of Mary, was nothing more than a messenger of God, His word, directed to Mary, a spirit from Him. So believe in God and His messengers and do not speak of a ‘Trinity’- stop [this], that is better for you- God is only one God, He is far above having a son, everything in the heavens and earth belongs to Him and He is the best one to trust. The Messiah would never disdain to be a servant of God, nor would the angels who are close to Him. He will gather before Him all those who disdain His worship and are arrogant: to those who believe and do good works He will give due rewards and more of His bounty; to those who are disdainful and arrogant He will give an agonizing torment...." - The Christians have had a difference of opinion over the so called divine nature of Jesus son of Mary (alaihi salaam) for almost 2000 years of their history, which has resulted in numerous sects among them. Now which Christians is Allah ﷻ addressing in the above ayah when He says "to those who believe and do good works He will give due rewards..." and how many and who among these will be forgiven, is His sole decision and all we can do is leave it to Him. Whats important to note is that this ayah teaches us that some non-Muslims among the Christian community will have opportunity to be forgiven.
Similarly Allah ﷻ gives hope of His Forgiveness and Mercy to non-Muslims of other religious communities, whether they be Jews, Christians, Buddhists, may be even Hindus or some groups in the remote regions of Earth that truly believe in One God, despite the fact that they may be unconsciously attributing divinity to other beings or forces in their worship due to Him: (Al Quran 2:62) The [Muslim] believers, the Jews, the Christians, and the Sabians- all those who believe in God and the Last Day and do good- will have their rewards with their Lord. No fear for them, nor will they grieve." - The criteria of salvation lies in the 3 factors for people of all communities: “who believe in God, the Last day and do good” - i.e. those who believe in one God, believe in the Day of Judgment and are concerned about their accountability, as a result of which they behave righteously in this life, whether they are Muslim believers or believers from others religious communities including Jews and Christians, they will be successful in the hereafter.
What about the “Good” Kaafir or Disbelievers?
In classical Arabic a Kaafir means someone who is an "outright disbeliever" or "bent on denying the truth". This term means someone who attempts to bury and hide the truth, someone who knows the truth yet rejects it.
They are those who do not seriously consider accountability before Allah ﷻ on judgment day which equals to denial in the existence of hereafter and belief in Allah ﷻ, and those who disbelieve in Allah ﷻ do not have any real faith, such people are only concerned with temporal world which is not the purpose of humankind’s creation. Therefore, belief in Allah ﷻ and accountability before Him is what makes your life have any value, if whatsoever. The world and all its wealth and attractions is of no value in the sight of Allah ﷻ if there is no faith in people’s hearts, as a prophetic hadith teaches us: “If the world to Allah was worth of a mosquito's wing, then He would not allow the disbeliever to have a sip of water from it.” This statement makes it clear that in the sight of Allah ﷻ the only thing in this world that is of any real value is called faith, and if that is denied by the hearts that are made for it then they can take this world as much as they like but in the hereafter they will have no share. The Quran teaches that such people will attempt to ransom themselves on judgment day to escape punishment of hell fire: (Al Quran 3:91) “Verily, as for those who are bent on denying the truth (kaafirs) and die as deniers of the truth (kaafirs) - not all the gold on earth could ever be their ransom. It is they for whom grievous suffering is in store; and they shall have none to help them.” In his Message of the Quran, Muhammad Assad comments on this verse: “some of the Quran commentators are of the opinion that what is meant here are otherwise good actions in this world (and, in particular, efforts and possessions spent for the sake of helping one's fellow-men), on the strength of which such stubborn "deniers of the truth" might plead for God's clemency on the Day of Judgment - a plea that would be rejected on the ground of their deliberate denial of fundamental truths.” - These non-Muslims who will live life of a denier and die as deniers will attempt to release themselves from Allah's punishment which will be of no use, because whatever righteous deeds they may have done were done based on no real faith in Allah ﷻ or the hereafter, hence based on justice they will be given what they deserve.
 Riyad as-Saliheen Book 1, Hadith 477
 Message of the Quran - Surah Al-'Imran (The House of Imran) 3:91 - Asad 1980