Firstly, The Christians are disbelievers
“Surely, they have disbelieved who say: ‘Allaah is the Messiah [‘Eesa (Jesus)], son of Maryam (Mary).’”
[al-Maa'idah 5:72]
“Surely, disbelievers are those who said: ‘Allaah is the third of the three (in a Trinity).’”
[al-Maa'idah 5:73]
And there are other texts which speak of their kufr (disbelief) and misguidance.
Among the verses which speak of their ultimate destiny is the last of the verses in the passage referred to by the questioner, where Allaah says (interpretation of the meaning):
“But those who disbelieved and belied Our Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.), they shall be the dwellers of the (Hell) Fire”
[al-Maa'idah 5:86]
and 109.1-6 Kathir - Ibn Al Kathir
The Declaration of Innocence from Shirk
This Surah is the Surah of disavowal from the deeds of the idolators.
It commands a complete disavowal of that. Allah's statement, قُلْ
يأَيُّهَا الْكَـفِرُونَ
(Say: "O disbelievers!") includes every disbeliever on the face of the
earth, however, this statement is particularly directed towards the
disbelievers of the Quraysh. It has been said that in their ignorance
they invited the Messenger of Allah to worship their idols for a year
and they would (in turn) worship his God for a year. Therefore, Allah
revealed this Surah and in it He commanded His Messenger to disavow
himself from their religion completely Allah said, لاَ أَعْبُدُ مَا
تَعْبُدُونَ
(I worship not that which you worship.) meaning, statues and rival
gods. وَلاَ أَنتُمْ عَـبِدُونَ مَآ أَعْبُدُ
(Nor will you worship whom I worship.) and He is Allah Alone, Who has
no partner. So the word Ma (what) here means Man (who). Then Allah
says, وَلاَ أَنَآ عَابِدٌ مَّا عَبَدتُّمْ وَلاَ أَنتُمْ عَـبِدُونَ مَآ
أَعْبُدُ
(And I shall not worship that which you are worshipping. Nor will you
worship whom I worship.) meaning, `I do not worship according to your
worship, which means that I do not go along with it or follow it. I
only worship Allah in the manner in which He loves and is pleased
with.' Thus, Allah says, وَلاَ أَنتُمْ عَـبِدُونَ مَآ أَعْبُدُ
(Nor will you worship whom I worship.) meaning, `you do not follow the
commands of Allah and His Legislation in His worship. Rather, you have
invented something out of the promptings of your own souls.' This is
as Allah says, إِن يَتَّبِعُونَ إِلاَّ الظَّنَّ وَمَا تَهْوَى
الاٌّنفُسُ وَلَقَدْ جَآءَهُم مِّن رَّبِّهِمُ الْهُدَى
(They follow but a guess and that which they themselves desire,
whereas there has surely come to them the guidance from their Lord!)
(53:23) Therefore, the disavowal is from all of what they are
involved. For certainly the worshipper must have a god whom he
worships and set acts of worship that he follows to get to him. So the
Messenger and his followers worship Allah according to what He has
legislated. This is why the statement of Islam is "There is no God
worthy of being worshipped except Allah, and Muhammad is the Messenger
of Allah." This means that there is no (true) object of worship except
Allah and there is no path to Him (i.e., way of worshipping Him) other
than that which the Messenger came with. The idolators worship other
than Allah, with acts of worship that Allah has not allowed. This is
why the Messenger said to them, لَكُمْ دِينُكُمْ وَلِىَ دِينِ
(To you be your religion, and to me my religion.) This is similar to
Allah's statement, وَإِن كَذَّبُوكَ فَقُل لِّى عَمَلِى وَلَكُمْ
عَمَلُكُمْ أَنتُمْ بَرِيئُونَ مِمَّآ أَعْمَلُ وَأَنَاْ بَرِىءٌ مِّمَّا
تَعْمَلُونَ
(And if they belie you, say: "For me are my deeds and for you are your
deeds! You are innocent of what I do, and I am innocent of what you
do!") (10:41) and He said, لَنَآ أَعْمَـلُنَا وَلَكُمْ أَعْمَـلُكُمْ
(To us our deeds, and to you your deeds.) (28:55) Al-Bukhari said, "It
has been said, لَكُمْ دِينَكُمْ
(To you be your religion.) means disbelief. وَلِىَ دِينِ
(and to me my religion.) means, Islam. This is the end of the Tafsir
of Surat Qul ya Ayyuhal-Kafirun.