Factually, who were the "People of the Book" here on earth ? The Quran also provide answers when the last judgment is made. Were the "Trinitarians" included among Christians in the "proper sense".

Shakir trans. (U of Mich)

The Cow
1.[2.62] Surely those who believe, and those who are Jews, and the Christians, and the Sabians, whoever believes in Allah and the Last day and does good, they shall have their reward from their Lord, and there is no fear for them, nor shall they grieve.

The Dinner Table
1.[5.69] Surely those who believe and those who are Jews and the Sabians and the Christians whoever believes in Allah and the last day and does good-- they shall have no fear nor shall they grieve.
The Jews, Christians and Sabians are classed together in these two verses - "they shall have no fear nor shall they grieve."

On the other hand, those who associate others with Allah have a great deal to fear.

The Cattle
1.[6.22] And on the day when We shall gather them all together, then shall We say to those who associated others (with Allah): Where are your associates whom you asserted?

Jonah
1.[10.28] And on the day when We will gather them all together, then We will say to those who associated others (with Allah): Keep where you are, you and your associates; then We shall separate them widely one from another and their associates would say: It was not us that you served:

The Bee
1.[16.86] And when those who associate (others with Allah) shall see their associate-gods, they shall say: Our Lord, these are our associate-gods on whom we called besides Thee. But they will give them back the reply: Most surely you are liars.
2.[16.100] His authority is only over those who befriend him and those who associate others with Him.
Following is a complicated verse, which I'm parsing for my education with the help of Maududi's commentary. It includes the Muslims ("those who believe"), the Jews, Sabeans and Christians (the other "People of the Book"), the Magians

The Pilgrimage
1.[22.17] Surely those who believe and those who are Jews and the Sabeans and the Christians and the Magians and those who associate (others with Allah) -- surely Allah will decide between them on the day of resurrection; surely Allah is a witness over all things.
Maududi's trans. & commentary

Maududi trans. snip:

[17] As regards those who believed[23] and those who became Jews[24] and the Sabaeans[25] and the Christians[26] and the Magians[27] and those who committed shirk,[28] Allah will judge between them on the Day of Resurrection,"[29] for everything is in the sight of Allah. ... [18]
"As regards those who believed[23]"

23. This means the "Muslims" of every age who believed in the Prophets of Allah and His Books up to the time of Prophet Muhammad (Allah's peace be upon him): they included both the sincere Muslims and the wavering Muslims.
"and those who became Jews[24]"

24. See E.N. 72 of Chapter IV (An-Nisa).

[JMM: For context, we have to consider the text at 44-46 and notes 71-73]

[44-46] Have you ever considered the case of those who have been given a portion of the scriptures?[71] They themselves purchase deviation and wish you, too, to go astray from the Right Way: Allah knows your enemies well and Allah suffices you for protection and for help. Some of those, who have become Jews,[72] pervert[73] words out of their context and twist their tongues in order to malign the true Faith ....

71. About the scholars of the people of the Book the Qur'an at many places has used words to the effect: "They have been given a part of the knowledge of the Scripture". These words have been used because the scholars had actually lost a portion of their Scriptures and had become strangers to the spirit and the real aim and object of the portion left with them. The only interest they took, in these was confined to polemical controversies, minor details of Commandments and philosophical subtleties of creed. That is why they were ignorant of the true nature of religion and were void of its essence, though they were called "Divines" and "Rabbis" and were the acknowledged leaders of their community.

72. The words used are: "who have become Jews" and not "who are Jews," for originally they were "Muslims" just as the community of every Prophet is Muslim. Then afterwards they degenerated and became merely "Jews".

73. They were guilty of perversion in three ways: (1) They effected changes in the words of the Scriptures; (2) they distorted the meanings of the text with false interpretations, and (3) they would sit in the assemblies of the Holy Prophet and his Companions and afterwards make false reports of what they heard there in order to create mischief against them by distortion. They would thus spread misunderstandings about Islam and pervert people from joining the Islamic Community.
"and the Sabaeans[25]"

25. "Sabaeans": In ancient times two sects were known by this title:

(1) The followers of Prophet John, who were found in upper Iraq in large numbers and practiced baptism.

(2) The worshipers of stars, who ascribed their creed to Prophets ####h and Idris (peace be upon them) and believed that the elements were governed by the planets and the planets by the angels. Their center was at Harran with branches spread all over Iraq. These people have been well known for their knowledge of philosophy and science and their achievements in medicine.

Probably here the first sect is referred to, because the second sect was not known by this name at the time the Qur'an was revealed.
See, Gunduz, The Knowledge of Life: The Origins and Early History of the Mandaeans and Their Relations to the Sabians of the Qur'an and to the Harranians (1994); contra, Fratini & Prato, God-Fearers: A Solution to the Ancient Problem of the Identity of the Sabians (1983)

- to be continued -

Regards

Mike