Are the Christians who exist nowadays the closest to us in love and friendship?

The praise mentioned in these verses should not cause any confusion regarding the Christians or make us refrain from cursing them. The description in the verse does not include all Christians, rather it refers to a group among them who responded to the truth and were not too arrogant to follow it. This is what is implied by the context of the verses asked about: 

“Verily, you will find the strongest among men in enmity to the believers (Muslims) the Jews and those who are Al-Mushrikoon, and you will find the nearest in love to the believers (Muslims) those who say: “We are Christians.” That is because amongst them are priests and monks, and they are not proud.

And when they (who call themselves Christians) listen to what has been sent down to the Messenger (Muhammad), you see their eyes overflowing with tears because of the truth they have recognized. They say: “Our Lord! We believe; so write us down among the witnesses”

[al-Maa’idah 5:82-83 – interpretation of the meaning] 

These verses are speaking of some Christian people who, when they came to know the truth, became Muslim and declared their faith. 

The great scholar Ibn al-Qayyim said concerning these verses: 

What is meant is that the people described here, when they realized that he was the Messenger of Allaah according to the description that they had, they could not stop their eyes from weeping or their hearts from hastening to believe. 

With regard to cursing those among the Christians who do not believe in Muhammad (peace and blessings of Allaah be upon him), there is innumerable definitive evidence which points to that, such as the hadeeth narrated by al-Bukhaari and Muslim in their Saheehs from ‘Aa’ishah (may Allaah be pleased with her), which says that the Messenger of Allaah (peace and blessings of Allaah be upon him) said, during his final illness: “May Allaah curse the Jews and Christians, for they took the graves of their Prophets as places of worship.” How can they not be cursed when Allaah has described them in His Book as follows? 

“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]

 From a fatwa of Shaykh Ibn Ibraaheem. Majallat al-Buhooth al-Islamiyyah, 58/36-39.