"It is obvious that Jews patronize the Jews and Christians patronize the Christians , so why not Muslims patronize Muslims and support their own people . This verse is not telling us to be against Jews or Christians , but it is telling is that we should take care of our own people and we must support each other. In his Tafsir , Imam Ibn Kathir has mentioned that some scholars say that this verse was revealed after the battle of Uhud when Muslims had to set back . At that time , a Muslim from Madina said "I am going to live with the Jews so I shall be safe in case another attack comes on Madina ." , and another said "I am going to live with Christians so I shall be safe in case another attack comes on Madina" . So Allah (swt) revealed this verse reminding the believers that they should not seek the protection from others , but should protect each other(See Ibn Kathir , Al-Tafsir , Vol 2 page 68) "

"As regards the meaning of the "alliance" referred to here , which explains the reference to a believer's loss of his moral identity if he imitates the way of life of, or-in Quranic terminology-"allies himself" with, non-Muslims. However, as has been made abundantly clear in 60: 7-9 (and implied in verse 57 of this Surah), this prohibition of a "moral alliance" with non-Muslims does not constitute an injunction against normal, friendly relations with such of them as are well-disposed towards Muslims. It should be borne in mind that the term wall has several shades of meaning: "ally", "friend", "helper", "protector", etc. The choice of the particular term - and sometimes a -combination of two terms-is always dependent on the context." (Asad, The Message of the Quran)  

One explanation is that this is referring to the hypocrites : 'Oh ye who believe outwardly' , and they used to assist the polytheists and tell them about the secrets of the Muslims. As-Suddi said that this verse came down during the Battle of Uhud when Muslims were afraid that they were going to lose the battle and wanted to ally themselves with the Jews and Christians. (Source)

Since I am answering the "Ex-Surah 5 Muslim" I won't go into the rest of the verses dealing with the topic of alliance and friendship in Quran , by showing that Surah 5 itself does not teach that Muslims should not take Jews and Christians as friends , I believe this is satisfactory.

Islam makes it clear that friendship and good relations with Christians and Jews (in fact with all man-kind) is allowed and advocated , we should co-exist peacefully , but we should not take them as close companions , allies or guardians if it leads away from the path of Islam or to moral degeneration , and such a close companionship is recommended if by one's moral character you are leading your friend to the path of Islam , what I find hilarious about the claim Dr.Caner made is that the bible teaches the exact same thing , see here.

I recommend the reader to check out these short videos dealing with this misconception: 

(this response was written by a very kind Muslim brother)