Main question: Does the Quran say in verse 3:28 that Muslims are not allowed to be friendly with non-Muslims, unless to protect themselves (or, as Islamophobes call it to trick them into Islam)?

Short answer: No

Long answer: The Quran and Prophetic tradition already clearly establish the difference between peaceful non-Muslims and hostile non-Muslims.

Al-Tabari stated in his Tafsir of 3:28:

Do not, O believers, take the disbelievers as a source of help and support or ally yourself with them in support of their religion, supporting them against the Muslims instead of the believers, and telling them about the Muslims’ weak points, for whoever does that “will never be helped by Allah in any way”. What is meant is that he has disavowed Allah and Allah has disavowed him because of his apostasy from His religion and his becoming a disbeliever. “except if you indeed fear a danger from them” [Aal ‘Imraan 3:28], that is, unless you are under their rule and you fear that they may kill you, so you pay lip service to giving them support, whilst concealing enmity towards them in your hearts, and you do not support them in what they are following of disbelief or help them against any Muslim in any way. (Tafsir al-Tabari 3/140)

In short, this verse is talking about supporting disbelievers against Muslims which is forbidden because it is treachery. The same also applies to verse 5:51, and verse 4:144 also gives the context for that (see verse 4:141) talking about hostile non-Muslims.

It should also be noted that the Prophet (SAW) did order the early Muslims to be in guardianship or “wilaya” of non-Muslims, more specifically under the lordship of King Najashi, the Negus of Abyssinia who the Prophet (SAW) described as a “just, merciful ruler who does no harm to his subjects” and thus ordered the Muslims who were fleeing from persecution to live under his guardianship, to which he agreed and refused to hand them over to the Quraysh.

Furthermore, the Quran states regarding peaceful non-Muslims:

“Allah does not forbid you from dealing kindly and fairly with those who have neither fought nor driven you out of your homes. Surely Allah loves those who are fair.” (Quran 60:8)

The Arabic word used here is “tabarruhum” or plural for “birr” which simply refers to all forms of goodness, including charity, friendship, and many others. Allah also uses this term to mandate treating parents well in verse 29:8, showing how powerful the term is.

“Allah only forbids you from befriending those who have fought you for ˹your˺ faith, driven you out of your homes, or supported ˹others˺ in doing so. And whoever takes them as friends, then it is they who are the ˹true˺ wrongdoers.” (Quran 60:9)

What do exegetes of the Quran say about relations with peaceful non-Muslims?

Al-Tabari states:

“The meaning of ‘Allah does not forbid you from those who did not fight you in religion’ are all types of denominations and faiths, that you be kind to them, have good relations with them, and be fair to them… It is all who fit that description, so the verse is not restricted to others. It does not mean those who say it is abrogated.” (Tafsir al-Tabari 22/574)

Al-Qurtubi states:

“This verse is a concession from Allah Almighty in maintaining relations with those who are not hostile to the believers and do not fight them… Most of the exegetes say the verse is operative.” (Tafsir al-Qurtubi 18/59)

The verse in question was revealed in the context of Asma bint Abu Bakr

Asma’ bint Abi Bakr reported: My mother, who was an idolater, came to me hoping for good treatment during the truce of the Prophet, peace and blessings be upon him, so I asked him, “Shall I keep relations with her?” The Prophet said: Yes, keep good relations with her." (Sahih Bukhari 5978)

In short: Verse 3:28 as well as 4:144 and 5:51 and other similar verses only prohibit supporting hostile disbelievers against the Muslims, has nothing to do with casual relations, otherwise Verse 5:5 which permits marriage between a Muslim man and Christian/Jewish woman, which the Quran also calls a union of “affection and mercy” wouldn’t be permitted either.