Who made up the term ‘Rafida’? Was it Zaid, son of Ali? And is it true that he used to befriend Abu Bakr and Umar?
In the Name of Allah, the All-Beneficent, the All-Merciful.
May Allah bless Muhammad and his Family and damn their enemies.
Such a false claim is based on a silly and weak narration by the so-called ‘Ahlul-Sunnah’  found within a legal verdict issued by the Mufti of Egypt or the dean of Al Azahar mosque in Cairo. However, if you look carefully on page 11 of the same reference, you will find that the person who wrote the introduction of the book cited the sources of the narration, which are all ‘Sunni’ sources. He said:
In the history account reference by Al Yafiaai, a ‘Sunni’, he stated that: when Zaid wanted to revolt, a group of people approached him and said: ‘We would join you if you renounce Abu Bakr and Omar.’ So he replied that he would not do so, so they replied in turn: ‘Then we would reject you.’ Zaid then said: ‘Go away, as you are the Rafida.’ The group that stayed with him was known as the Zaidis.
Musnad Zaid bin Ali, page 11
The truth of the matter is that the term ‘Rafida’ was widely known before the account of that fabricated incident by many years. Ibn Al Aatham narrated that
Muawiya sent a letter to Amr, son of Al Aas (may the wrath of Allah be upon them both), in which the following statement came: “The Rafida of Yemen, Basrah, Kufa and Hejaz are being assembled in aid of Ali, son of Abi Talib.
Al Futooh, by Ibn Aatham, vol. 2, page, 382
The term Rafida was used to describe the followers of the Commander of the Believers (peace be upon him) as evidenced by the usage of the term by Muawiya himself approximately 80 years before the fabricated account that was alleged to have been narrated by Zaid, son of Ali, as reported by the alleged narration that we mentioned earlier.
In fact, the Shia reference accounts talk about an altogether different narration related to Zaid, son of Ali, and his position against those who mixed their faith with loyalty to the pure household of the Prophet on the one hand and their affection to Abu Bakr and Omar on the second hand.
In Rijal Al Kishi you will find this narration:
Sudayr said that he went together with Salamah, son of Kuhail, and others to meet Imam Muhammad al-Baqir (peace be upon him). Imam Muhammad al-Baqir (peace be upon him) was with his brother, Zaid, son of Ali. Some of those who were in the council, said to Zaid: ‘We are loyal to Ali, Hassan and Hussain and renounce their enemies.’ Zaid said: ‘Good!’ Then they said: ‘But we also are loyal to Abu Bakr and Omar and renounce their enemies. Zaid then turned towards them and said: ‘So you also renounce Fatima? You have cut short our case, may Allah cut you out.’
Rijal Al Kishi, page 236.
From that moment, they became known as the ‘Batriya’, because the verb cut off or cut short in Arabic is ‘Batara’. Therefore, the term ‘Batriya’ means those who mix up their loyalty to the pure Household of the Prophet (peace be upon him and his family) together with the endorsement and recognition of their enemies like Abu Bakr, Omar and the rest of the gang of Saqeefa and whoever approved it.
The Office of Sheikh al-Habib
-  Musnad Zaid bin Ali, page 46.