Based on the meanings explained by the Salaf, and the Ahlus Sunnah (Ash'ari & Maturidi) scholars.
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Beginning with the Name of Allah, The Most Gracious, The Most Merciful 
FOOTNOTES: Beginning with the Name of Allah, The Most Gracious, The Most Merciful
 – Surah Al-Kafirun is Makkan. It contains 1 rukoo’, 6 verses, 26 words, and 94 letters.
Circumstances of revelation: A group from the [infidels of the] Quraysh told the Master of the worldsﷺ , ‘You follow our religion and we will follow your religion. For an year, you worship whom we worship (i.e., the idols), and for an year we shall worship whom you worship (Allah, the One & Only true God).’ The Master of the worlds ﷺ said [what means], ‘I seek refuge with Allah that I attribute a partner to Him.’ They said, ‘Then at least just touch one of those we worship [i.e., one of the idols]; and we shall acknoweldge you [i.e., your prophethood] and worship whom you worship.’ On this, this blessed surah was revealed and the Master of the worlds ﷺ went to the Holy Haram (the Holy Mosque in Makkah) and that group from the Quraysh was present there. When the Master ﷺ read this surah to them, they became upset and got hurt at the hands of the Master ﷺ and his companions.
 – Specifically the kafirs are addressed here, who are bereft of belief in the knowledge of The Almighty.
 – Meaning ‘for you, your kufr, and for me, my tawhiid and sincerity’ and by this the intention is threatening [of hellfire]; وَھٰذِہِ الاٰ یَـة مَنْسُوْخَة بِآ یَـة الْقِتَالِ – and this verse has been abrogated by the verse of war.
[Translator’s Note: Further information on verse 6 taken from Imam Fakhruddin Ar-Razi’s Mafaatiih Al-Ghayb, and Imam Qurtubi’s Jaami’ Al-Ahkaam Al-Quran:
On the meaning of His Ta’ala’s saying (لَكُمْ دِينُكُمْ وَلِيَ دِينِ) (To you your deen, to me my deen) – there are matters relating to it.
The First Case: Ibn ‘Abbas said: To you, your kufr against Allah, and to me, Tawhiid and ikhlas (sincerity) to Him. Then if it is said, “Then can one say, he [The Blessed Master ﷺ] permitted them to stay on kufr?” we say, “Never – for he, ‘alaihis salam, wasn’t sent but for prohibiting kufr, so how can he permit it?” But the intention from it [saying thusly] is one of these:
Firstly: The intention from it is threatening [of Allah’s Wrath] and this goes along the same theme of the [disdainful expression in the] verse (اعْمَلُوا مَا شِئْتُمْ) (Do as you please – 41:40)
Secondly: As if to say: I am the prophet sent to you so that I invite you to the truth and salvation. Then if you do not accept from me [what I bring], and do not obey me, at least leave me [alone] and do not invite me to shirk (paganhood).
Thirdly: (To you, your deen) – If you think perdition’s better for you, then stay upon it. (To me, my deen) – Because I simply won’t leave it.
The Second Saying: In the tafsiir of the verse, accountability is implicated by deen (religion), that is to say, ‘to you your account and to me my account’ (i.e., ‘you are accountable for your ways and I am accountable for mine’) as verily, none of us shall be held accountable for deeds of the other.
The Third Saying: In this discussion, the genitive can be superimposed upon [according to the rules of Arabic language], thereby implying: to you the recompense for your deen (religion), and to me the recompense for my deen; and [the implication from Allah is:] ‘the recompense for their deen is perdition and penalty, just as the recompense for your deen [O Beloved Prophet] is honor and reward’.
The Fourth Saying: Deen [also implies] it is recompense [in and of itself] (وَلَا تَأْخُذْكُم بِهِمَا رَأْفَةٌ فِي دِينِ اللَّهِ) (and do not be taken by pity for them in Allah’s religion 24:2) meaning in implementing the hadd [penalty]. That is to say, ‘For you is punishment from my God, and for me is punishment from your idols. But your idols are lifeless objects. Therefore, I do not fear the punishment from your idols; but you have good reason to be afraid of the punishment of The Omnipotent Almighty of the heavens and the earth [that is, Whose Will & Power control the universe].
The Fifth Saying: Is “deen is dua” (فَادْعُوا اللَّهَ مُخْلِصِينَ لَهُ الدِّينَ) (Then dua [towards] (worship/call upon) Allah, completely being His slave alone – 40:14) – implying “your dua is for you”; (وَمَا دُعَاءُ الْكَافِرِينَ إِلَّا فِي ضَلَالٍ) (The dua of kafirs is nothing but waste – 13:14); (إِن تَدْعُوهُمْ لَا يَسْمَعُوا دُعَاءَكُمْ وَلَوْ سَمِعُوا مَا اسْتَجَابُوا لَكُمْ ۖ) (If you call upon them, they can’t hear you, and even if they did, they would not be able to grant your desire. 35:14). As long as you stay in this state, they (the idols) won’t be able to harm you. However, on the Day of Judgment they shall be granted tongues and they shall disavow from your paganhood. But my God says: (وَيَسْتَجِيبُ الَّذِينَ آمَنُو) (And He grants the dua of those who believe – 42:26); (ادْعُونِي أَسْتَجِبْ لَكُمْ) (Dua (call unto) to Me and I shall grant you – 40:60); (أُجِيبُ دَعْوَةَ الدَّاعِ إِذَا دَعَانِ) (I grant the dua of the caller when he calls – 2:186)
The Sixth Saying: Religion is convention [tradition/habit]. As the poet says:
“As she was told, she mounted a saddle – It shall always be her deen (custom) as it is mine.” (English translation as phrase is adjusted to incorporate the message of the Arabic verse)
The meaning [based on this interpretation of “deen”] is to say, “To you your traditions that you inherited from your forefathers and satans; and to me the traditions I have taken from angels and Divine Revelation. Then every one of us can remain upon his ways, until you guys meet with hellfire and satans, and I meet with angels and paradise!”
The Second Case: [To you your religion] implies limitation, and its meaning is ‘your religion is ONLY for you and for no one else; my religion is ONLY for me and for no one else.’ And this is an indicator towards His saying (وَأَن لَّيْسَ لِلْإِنسَانِ إِلَّا مَا سَعَىٰ) (There isn’t for man except that for which he strived 53:39); (وَلَا تَزِرُ وَازِرَةٌ وِزْرَ أُخْرَىٰ) (And no bearer of burdens shall bear the burden of another. 6:64) – meaning to say ‘I am responsible for [receiving] revelation and propagation, and you are responsible for compliancy and acceptance. Then, when I have done what I was responsible for, I am acquited of my responsibility. And your persistence on your kufr shall certainly not lead to any harm to me by it.’
Another Case: It is customary for people to draw parallels with this ayah in matters of agreements [and debates etc.]. And this is NOT permissible. Because He, Ta’ala, did NOT send down the Quran for drawing parallels to it but rather for contemplating on it, and then to act in accordance to it. And Allah Subhanahu wa Ta’ala knows and judges best; and may Allah raise the ranks of our Master Muhammad, and his noble progeny and companions.
His Ta’ala’s saying (لَكُمْ دِينُكُمْ وَلِيَ دِينِ) (To you your deen, to me my deen) – Is in the meaning of a threat, and it is similar to His Ta’ala’s saying [and teaching us to say] (لَنَا أَعْمَالُنَا وَلَكُمْ أَعْمَالُكُمْ) (To us, our deeds; and to you, your deeds – 2:139) meaning to say ‘If you are happy with your deen, we are happy with our deen’. And this was BEFORE the command for war, and has been abrogated by the verse of the sword. And it is said, the entire surah is abrogated. And it is [also] said, nothing from it is abrogated as it is information [i.e., a statement of fact] and the meaning of (to you, your deen) is to say ‘[to you,] the recompense for your deen and to me, the recompense for my deen’. And their [false] religions are [also] called “deen” because they believe in them and accept them. And it is said: The meaning is ‘to you, your recompense, and to me, my recompense’ because “deen” is recompense.]