Muslims and Christians are like to rays of light coming from the same source.

60:8] GOD does not enjoin you from befriending those who do not fight you because of religion, and do not evict you from your homes. You may befriend them and be equitable towards them. GOD loves the equitable.

[60:9] GOD enjoins you only from befriending those who fight you because of religion, evict you from your homes, and band together with others to banish you. You shall not befriend them. Those who befriend them are the transgressors.

Thus, we learn that we are only enjoined from befriending those who fight us because of religion. Let's go back to the verse immediately after 5:51, to see if it now sheds some more light on the issue.

[5:57] O you who believe, do not befriend those among the recipients of previous scripture who mock and ridicule your religion, nor shall you befriend the disbelievers. You shall reverence GOD, if you are really believers.

God teaches us throughout the Quran that there are righteous Jews and Christians. So, if we think we are righteous, and they are righteous, what could possibly be the problem between us, or obstacle for us to be friends?

[7:159] Among the followers of Moses there are those who guide in accordance with the truth, and the truth renders them righteous.

[5:46] Subsequent to them, we sent Jesus, the son of Mary, confirming the previous scripture, the Torah. We gave him the Gospel, containing guidance and light, and confirming the previous scriptures, the Torah, and augmenting its guidance and light, and to enlighten the righteous.

[5:47] The people of the Gospel shall rule in accordance with GOD's revelations therein. Those who do not rule in accordance with GOD's revelations are the wicked.

[2:62 & 5:69] Surely, those who believe, those who are Jewish, the Christians, and the converts; anyone who (1) believes in GOD, and (2) believes in the Last Day, and (3) leads a righteous life, will receive their recompense from their Lord. They have nothing to fear, nor will they grieve.

[3:113-114]. They are not all the same; among the followers of the scripture, there are those who are righteous. They recite GOD's revelations through the night, and they fall prostrate.

They believe in GOD and the Last Day, they advocate righteousness and forbid evil, and they hasten to do righteous works. These are the righteous.

[3:199] Surely, some followers of the previous scriptures do believe in GOD, and in what was revealed to you, and in what was revealed to them. They reverence GOD, and they never trade away GOD's revelations for a cheap price. These will receive their recompense from their Lord. GOD is the most efficient in reckoning.

We learn, however, from the Quran that the Christians are closer to the believers (submitters-Muslims) than the Jews. This is just a statement of fact by God almighty, that we can still witness during our time. God is the best knower of the emotional structure of His creations and therefore was this statement of fact in 5:82. We can witness from the conflict in the Middle East for example , how very emotional the Jews get and how they react to conflicts with their friends, their enemies or even among themselves inside Israel.