The emphasis being on "what was revealed to them", not scriptures adulterated and changed with the word of man ("they do not exchange the verses of Allah for a small price"). What was revealed to them is that they should believe in and worship one God, with no sons, no 3-in1s, no associates/sharers whatsover in His Exclusive Divinity, and that they must obey the messenger, and that there was a messenger to come. It also says, and they believe in "what was revealed to you", you being the prophet Muhammad, peace and blessings of Allah be upon him. To believe in that (the Qur'an), you have to accept the Messenger it was revealed to (Muhammad peace be upon him) and follow the commands contained therein. And many Christians at the time of the Prophet did exactly that.
It does not include nowadays Christians who worship a trinity while still saying they believe in one God, and who also reject the final Messenger of Allah, and the final unchanged word of Allah.
Asalaamu alaikum,
This is the Tafsir that I've read as posted on qtafsir dot com from Tafsir Ibn Kathir. Since I'm so new, I can not post the arabic script text so please excuse me for that. The red text is a highlight added by me.
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The Condition of Some of the People of the Scriptures and their Rewards
Allah states that some of the People of the Book truly believe in Him and in what was sent down to Muhammad , along with believing in the previously revealed Books, and they are obedient to Him and humble themselves before Allah.
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(They do not sell the verses of Allah for a small price) ﴿3:199﴾, for they do not hide what they know of the glad tidings about the description of Muhammad , his Prophethood, and the description of his Ummah. Indeed, these are the best people among the People of the Book, whether they were Jews or Christians. Allah said in Surat Al-Qasas,
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(Those to whom We gave the Scripture before it, they believe in it (the Qur'an). And when it is recited to them, they say: "We believe in it. Verily, it is the truth from our Lord. Indeed even before it we were Muslims. These will be given their reward twice over, because they are patient,) ﴿28:52-54﴾. Allah said,
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(Those to whom We gave the Book, recite it (follow it) as it should be recited (i.e. followed), they are the ones who believe therein.) ﴿2:121﴾,
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(And of the people of Musa there is a community who lead with truth and establish justice therewith.) ﴿7:159﴾,
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(Not all of them are alike; a party of the people of the Scripture stand for the right, they recite the verses of Allah during the hours of the night, prostrating themselves in prayer.) ﴿3:113﴾, and,
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(Say: "Believe in it (the Qur'an) or do not believe (in it). Verily, those who were given knowledge before it, when it is recited to them, fall down on their faces in humble prostration.'' And they say: "Glory be to our Lord! Truly, the promise of our Lord must be fulfillled.'' And they fall down on their faces weeping and it increases their humility.) ﴿17:107- 109﴾.
These qualities exist in some of the Jews, but only a few of them. For instance, less than ten Jewish rabbis embraced the Islamic faith, such as `Abdullah bin Salam. Many among the Christians, on the other hand, embraced the Islamic faith. Allah said,
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(Verily, you will find the strongest among men in enmity to the believers the Jews and those who commit Shirk, and you will find the nearest in love to the believers those who say: "We are Christians.'') ﴿5:82﴾, until,
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(So because of what they said, Allah rewarded them Gardens under which rivers flow (in Paradise), they will abide therein forever) ﴿5:85﴾. In this Ayah,
Allah said,
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(for them is a reward with their Lord) ﴿3:199﴾.
When Ja`far bin Abi Talib recited Surah Maryam ﴿chapter 19﴾ to An-Najashi, King of Ethiopia, in the presence of Christian priests and patriarchs, he and they cried until their beards became wet from crying. The Two Sahihs record that when An-Najashi died, the Prophet conveyed the news to his Companions and said,
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(A brother of yours from Ethiopia has passed, come to offer the funeral prayer.) He went out with the Companions to the Musalla lined them up in rows, and after that led the prayer.
Ibn Abi Najih narrated that Mujahid said that,
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(And there are, certainly, among the People of the Scripture), refers to those among them who embraced Islam. `Abbad bin Mansur said that he asked Al-Hasan Al-Basri about Allah's statement,
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(And there are, certainly, among the People of the Scripture, those who believe in Allah).
Al-Hasan said, "They are the People of the Book, before Muhammad was sent, who believed in Muhammad and recognized Islam. Allah gave them a double reward, for the faith that they had before Muhammad , and for believing in Muhammad (after he was sent as Prophet).'' Ibn Abi Hatim recorded both of these statements. The Two Sahihs record that Abu Musa said that the Messenger of Allah said,
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(Three persons will acquire a double reward. )
He mentioned among them,
(A person from among the People of the Book who believed in his Prophet and in me.)
Allah's statement,
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(They do not sell the verses of Allah for a small price), means, they do not hide the knowledge that they have, as the cursed ones among them have done. Rather, they share the knowledge without a price, and this is why Allah said,
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(for them is a reward with their Lord. surely, Allah is Swift in account.)
Mujahid commented on the verse,
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((Surely, Allah is) swift in account), "He is swift in reckoning,'' as Ibn Abi Hatim and others have recorded from him.