Praise be to Allah, and peace and blessings be upon the Messenger of Allah.
Whoever is born into Islam, believes firmly in Allah and His Messenger, and fulfills the obligations that Allah has prescribed, then his faith is valid. He is not required to fall into doubt or to re-examine the truth of his religion after Allah has blessed him with guidance. Rather, what is required of him is to increase his faith by reflecting upon the Qur'an, contemplating the signs of Allah, and performing righteous deeds—not by doubting what has already become certain to him.
The majority of scholars have stated that the faith of a person who follows Islam through imitation (taqlid) is valid, provided that their belief is firm and free from doubt. The Prophet Muhammad ﷺ did not require those who embraced Islam to know philosophical or rational proofs or the methods of theological reasoning. Rather, he accepted from them sincere faith and submission to the teachings of Islam. For this reason, the Companions accepted the Islam of ordinary people without testing them in the finer points of creed or demanding that they provide rational evidence for what they believed.
This does not mean that a Muslim does not benefit from knowledge and reflection. On the contrary, the more a person learns about their Lord and reflects upon His Book, the stronger their certainty and faith become. However, this relates to the perfection and strengthening of faith, not to the validity of its foundation.
As for a Muslim who commits major sins, they do not leave Islam unless they commit something that nullifies their faith. If they die while affirming the oneness of Allah (Tawhid), they are under Allah's will: if He wills, He forgives them, and if He wills, He punishes them according to their sins. Ultimately, they will enter Paradise, because belief in the Oneness of Allah is the greatest cause of salvation and the foundation upon which all righteous deeds are built.
As for the non-Muslim, their righteous deeds in this world will not benefit them in the Hereafter as long as they die in disbelief, because the acceptance of deeds is conditional upon faith. Allah may reward them in this world with good health, provision, or other blessings because of their good deeds, but in the Hereafter they will have no reward while persisting in disbelief.
In summary: A Muslim whose faith is established is not required to investigate the truth of Islam in a way that leads them into doubt. Rather, they should remain steadfast in faith, perform righteous deeds, and seek beneficial knowledge that increases their certainty. According to the majority of scholars, the firm faith of one who follows Islam through imitation is valid. Whoever dies upon Tawhid will ultimately be among the people of Paradise, even if they are first punished for some of their sins. This is part of Allah's grace, justice, and perfect wisdom.
And Allah knows best.