The scholars who interpreted these passages as an invitation to accept Islam pointed out that the verses require that one have imaan in Allah. While this has been simply translated as 'belief' or 'faith', its meaning goes deeper than that. The Qur'an itself clarified this:
4:65 But no, by the Lord, they can have no real Faith (imaan), until they make thee judge in all disputes between them, and find in their souls no resistance against Thy decisions, but accept them with the fullest conviction.
Likewise, Imaam Ash-Shawkaani writes in his commentary on verse 2:62:
What is meant here by Imaan is what the Prophet (peace be upon him) said, "Imaan is to believe in Allah, His angels, His books, His messengers, and the Last Day, and to believe in divine destiny, both the good and the evil thereof", while no one is described as a believer except when he has entered the fold of Islam, therefore, whoever doesn't believe in Muhammad (peace be upon him) and doesn't believe in the Qur'an is not a believer, and whosoever of them believes in it, has become a Muslim/believer and he is no longer Christian, Jewish, or Sabian. (Shawkani, Fath Al-Qadeer: Mu'asasat Ar-rayan (Part 1), p. 122)
And Mufti Muhammad Shafi writes:
a closer look at this verse itself will show a distinct hint towards belief in prophethood because, in the terminology of the Qur'ân, only that 'Îman bil-lâh (belief in Allah) is valid, in which there is belief in everything told by Allah. The Qur'ân has made its terminology very clear in the following words:
So, if they (the Companions) believe in the like of what you (the Prophet saws) believe in, they have certainly found the right path - 2:137
It means that the kind of 'Îman the noble Sahâbah [companions] had is the only 'Îman which deserves to be called 'Îman bil-lâh. And it is obvious that 'Îman bir-rasûl [belief in the Messenger] was a great pillar of the edifice of their 'Îman. Therefore, the words: (whoever believes in Allah) are inclusive of the belief in the Messenger of Allah. (Shafi, Ma'ariful Qur'an, Maktaba-e-Darul-Uloom, Karachi, 2003, vol. 3, p. 224)
It is quite clear that if we take these verses of the Qur'an in context and understand them in light of other Qur'anic verses and Ahadith, as oppose to taking them in isolation, then there remains no confusion that the one true path in life is submitting to the will of the Creator and acting in accordance with His final message, which is Islam.
3. Abrogation
Aside from the above explanations given, some other scholars assert that this verse has been abrogated (in a very general sense of the word). While this may seem to be in conflict with the understanding presented above, in reality it is complimentary to the previous explanations. According to this explanation, when Islam was in its early stages and was not yet known to many people, these verses (2:62 & 5:69) were revealed to clarify that anyone who sought their Lord, using whatever guidance they found left by previous Prophets, would be rewarded. Later, when Islam spread and became known to the people, it was clarified that from that point onwards, people would have to accept the message of Islam when it reached them. Thus, it could be said that the previous verse was 'abrogated' in a general sense (more on abrogation is found here). The support for this view is found in various Tafsir, such as that of Imaam Abu Abdullah Al-Qurtubi (d. 1272 CE) who writes:
It is reported from Ibn Abbas that this ayat is abrogated by "If anyone desires anything other than Islam as a din [way of life], it will not be accepted from him." (3:85) Others said that it is not abrogated and that it is about those who believe in the Prophet, peace be upon him, and who are firm in their belief. (Al-Qurtubi, Tafsir Al-Qurtubi, Dar Al-Taqwa Ltd. 2003, vol. 1, p. 267)
This quote indicates that the interpretation attributed to Ibn Abbas and supported by some scholars, holds that verse 3:85 comes after verse 2:69 and abrogates it.
It should also be noted that Islam asserts that God will judge everyone according to their circumstances. Consequently, it is not for Muslims to say whether someone, either living or deceased, will enter hell unless with explicit proof from the Qur'an or Ahadith. The renowned scholar, Imaam Ibn Al-Qayyim Al-Jawziyyah (d. 1350CE), said concerning non-muslims who did not receive the clear message of Islam:
We cannot rule whether such people are believers or unbelievers, because disbelieving means to deny something, while in their case, they did not know about the message from the first instance. As they were neither believers nor unbelievers, they should have a different ruling on the Day of Judgment.
Even if we were to say that they are unbelievers, then we would still have to say that the precondition for unbelievers to be punished in the Hereafter has not been realized in their case. They have to be warned first. Allah will not punish people without a previous warning. This warning should be in the language that the person understands. (Tarîq al-Hijratayn and Ahkâm ahl al-Dhimmah)
Similarly, the IslamToday.com fatwa service writes:
Non-Muslims who never heard the message of Islam are known as ahl al-fatrah. God says: 'Nor would We punish until We had sent a messenger (to give warning).' [Sûrah al-Isrâ: 15]
Many scholars, including Ibn al-Qayyim, Ibn Kathîr and Ibn Bâz, have adopted the saying that the people who have never had an opportunity to come to know about Islam will be tested by God on the Day of Judgment. Those who pass the test and obey the commands will go to Paradise and those who are disobedient will go to Hell.
God knows best who has heard His message properly and rejected it and who has not done so. The most we can say that it is obligatory for all people to accept Islam and that anyone who knowingly rejects the truth of Islam is condemned in the Hereafter. However, it is not our place to state exactly what God is going to do with each and every individual on the Day of Judgment. God is the only one who knows the hearts of people and their circumstances, and He is the only one who will sit in judgment. We must trust in Him.
Hopefully, this article will clarify any confusion surrounding the Islamic concept of salvation and the meaning of these Qur'anic verses.
Allah knows best