What is the ruling on greeting with the salam one who does not belong to Islam?

Question:
The brother questioner says: Honorable Shaykh, may Allah’s peace, mercy, and blessings be upon you. After that, I love you for the sake of Allah, and my question is that I have an old colleague whom I once advised, but he cursed me and then followed that by saying that he is not a Muslim and that he is a Jew. He says: So I left that person, and then later I passed by him and met him. When I meet him, I greet him, saying, for example, “As-salamu alaykum.” Do I sin in doing so?

Answer:
First, may Allah love you for the sake of the one you loved, for the Messenger (peace and blessings be upon him) said in the hadith: Among them are two men who loved each other for the sake of Allah, they gathered for that and parted for it. He (peace and blessings be upon him) said: And he (peace and blessings be upon him) said that Allah will say on the Day of Resurrection: The ones who love for My majesty, today in My shadow. So my advice to the listeners and others is to love for the sake of Allah, to advise one another to truth, to give sincere advice constantly, and not to be bored or lazy. As for this one who insults you, when you advised him he did not accept the advice and said he is not a Muslim and that he is a Jew, and so on. With this speech, he has become an apostate; he has apostatized from Islam from the very first pulpit, and he has become a disbeliever by his own admission, we seek refuge in Allah. You must not greet him after that; if you accept him, do not greet him, and if he greets you, do not return the greeting, because he has become a disbeliever. The Prophet (peace and blessings be upon him) said: They are Jews, People of the Book. So an apostate is even more deserving of not being greeted first and not having his greeting returned, because of his disbelief and his deserving of execution. It is obligatory to report his case; if he does not repent, his case must be reported to the authorities so that he is dealt with as apostates are dealt with, unless he repents and turns back from the falsehood he is upon. If you see that you can hint to someone you think can influence him to advise him and guide him to good, then you are doing well in this, perhaps Allah will guide him through these means. If he persists in the falsehood, the insults, and the claim that he is a Jew like this, it is not to be accepted; rather, his case must be reported to the authorities, to the court, to the committee, so that he is dealt with as he should be, through seeking his repentance and judging him with what the Shari'ah requires. Yes, we ask Allah for safety.