1. The name of Ameerul Mo'mineen Ali (AS) was mentioned in the Athaan during the time of the Prophet Muhammad (SAWA) as you can find it is Sunni books like Assalaafah Fi Akhbar al-Khilafah by al-Maraaghi, page 24. After the announcement of Ghadeer when the Prophet asked all companions to give allegiance to Ali, the first Athaan given by Bilâl was with Ashhadu Anna Ali Ameerul Mo'mineen.
Some opponents of Ali objected on that and complained to the Prophet saying : the sin of black woman (Bilâl) has added on Athaan. The Prophet rejected their complain and asked them : Then what did we announce ?
Clearly, the witness the Ali is Ameerul Mo'mineen is the soul of Ghadeer announcement and the spirit of Islam being the divine successor of the Prophet (SAWA).
2. This status of Ali is mentioned in many Sunni books like Musnad Ahmad Ibn Hanbal, volume of Fadha'il Ali Ibn Abi Talib, page 342 who narrated Hadeeth of Jaabir ibn Abdullah al-Ansaari, from the Prophet Muhammad (SAWA): I saw on the gate of Paradise a writing : LAA ELAAHA ILLALLAH, MUHAMMAD IS RASOOLULLAH, ALI IS BROTHER OF RASOOLULLAH.
3. A man came to the Prophet (SAWA) and said: I saw and heard Salman (al-Farisi) mentioning is Athaan after the witness of Risalah, a witness of Wilayah to Ali. The Prophet replied him: What you heard (from Salman) is good.
( عنوان الصحيفة Onwan al-Saheefah, page 81.
4. We have authentic Hadeeth from the Prophet (SAWA) : When you mention me with Prophet hood, mention Ali as Ameerul Mo'mineen.
5. Mentioning the name of Ali (AS) in Athaan is not matter of love because we love Fatimah and all the Infallible Imams, but we do not mention their name in Athaan, but it is a matter of following the orders of the Prophet to all Muslims to follow Ali.
6. All our great scholars say that mentioning Ali as Ameerul Mo'mineen in Athaan and Eqamah is recommended. We do have few Ulama who said that it is obligatory as a sign of faith but our present Maraaji' of Taqleed say it is Mustahab (recommended).
7. Those who claim mentioning the name of Ali in Athaan is Bid'ah are very far from the authentic evidence or they might be influenced by the books of others who are away from Ahlul Bayt (AS).