Shaikh al-Albani rahimahullah said:
“If it is said: is it allowed to to initiate other than the greeting of peace with a disbeliever? For example: ‘How are you this morning’ or ‘How are you this evening’ or ‘How are you’ and the likes. Then I say: that which is apparent to me, and Allah knows best, is that it is allowed because the prohibition mentioned in the Hadith [Muslim no. 2167] is only for salam. In general, what is only intended [by the Hadith] is the Islamic greeting which includes the Name of Allah, the Exalted. As comes in the statement of the Prophet(ﷺ):
السلام اسم من أسماء الله وضعه في الأرض فأفشوه بينهم
As-Salam (peace) is one of the Names of Allah Almighty which Allah has placed in the earth. Therefore spread the greeting among yourselves. Reported by Bukhari in Adab al-Mufrad (no. 989) and it will come [in as-Saheeha] no. 1894.
What supports what I have mentioned is the statement of ‘Alqamah: “Verily Abdullah (that is: Ibn Mas’ud) used to give greetings to the Persian businessmen with a gesture. Reported by Bukhari (no. 1104) and he gave the chapter title for it: A person greeting a dhimmi with a gesture. Its chain is Saheeh. So Ibn Mas’ud (may Allah be pleased with him) allowed initiating greetings with a gesture because it is not a greeting specific to Muslims. Likewise, it is allowed to greet them [the non-Muslims] with the likes of what I mentioned of wordings.
As for what was mentioned in some books of the Hanaabilah like ad-Daleel, that it is prohibited to also initiate the greetings [saying]: ‘How are you this morning or evening’ or ‘how are you’, then I do not know of an evidence for that from the Sunnah…” [Silsilatus-Saheeha (no. 704) 2/318]
He also said rahimahullah:
“…If it is necessary for you to initiate and you say to him: ‘Good morning’ or ‘Good evening’, then this is the exiting point [from this issue] and the subject of giving salam to the disbeliever ends…” [Silsilatul-Huda wan-Nur (no. 50)]
Faisal Ibn Abdul Qaadir Ibn Hassan