In the Quran Ibrahim has been known as a "Hanif" individual and the prophet has called the Muslim Ummah to follow his path. From the Islamic perspective there is no fundamental difference between holy religions, therefore following the religion of Ibrahim is actually the following of original Christianity and Judaism. It should be kept in mind that the prophet never opposed the teachings of true Christianity and Judaism; instead Islam shares a lot with these religions, like the issue of Qisas (compensation). But we all know that these religions and there books have been altered and distorted through history and the Christians and Jews contemporary to the prophet possessed these books, and if the Quran and prophet were to officially announce that Islam was following Christianity and Judaism, there were chances that the heads of these religions would take advantage of such an announcement, causing problems for the spread of Islam. But calling people to Prophet Ibrahim's message would not entail such difficulties, because not only was Ibrahim a very respected figure to Christians, Jews and Muslims, but also his religion no longer had anyone claiming to be a high figure in it. This way Islam would not face any problems by calling its followers of Prophet Ibrahim's religion.
Your question can be broken down into two questions:
1- Who are the "Hanifiyyun" and what does the word "Hanif" mean in the Quran?
2- Why was the Prophet called a "Hanif" and not a Christian?
In order to explain the first question we will shed some light on a few points:
1.1 When we refer to Arabic dictionaries we find that the term "Hanif" is used for one who seeks the truth and turns away from false religions. The meaning of "Hanif" covers those who have not been influenced by religious and tribal bias to put aside the truth and still seek it.
Prophet Ibrahim was among the "Hanifiyyun" which sought the truth. In one hadith by Imam Sadiq (as), in interpretation of verse 67 from Surah Ale Imran, he says: "Ibrahim was a sincere person who never went after worshipping the idols." This is why his path is known as a "Hanif" path in the Quran.
1.2 But did the followers of Ibrahim actually come together and establish an organized religion and create a community under the name of the ‘Hanifiyyun’ in which they would practice their religion's teachings the same way the Christians or Jews did? History does not show such a thing at least at the time of the prophet (pbuh), because all the things necessary for an organized religion with such a name were missing at the advent of Islam, things like:
1- A leader that would preside over the community and the followers of the religion.
2- A book or other religious text that could be referred to when encountering a matter of dispute.
3- Temples or places of worship where the believers could carry out there religious ceremonies and worship God.
4- Scholars that people could refer to when they could not solve their religious problems.
Despite the fact that many of his people considered Ibrahim their religious leader at that time, but no book or scripture has been attributed to him, not even an altered and distorted one, unlike the Christians and Jews that had books like the Bible and the Torah. Moreover there is no specific place where they would worship God like the Churches, Synagogues and Mosques other than the Ka'aba. They also didn't have scholars or clergymen that would preach the religion like Priests and Monks. Therefore Ibrahim did not establish a community comprised of the believers, but rather those people who would not worship the idols and would not accept the wrong traditions of their society considered themselves followers of this great prophet of Allah without gathering together. The ahadith refer to these people as the "Hanifs”. Some of the teachings Ibrahim called his people to were practiced before the advent of Islam. For example the ritual of Hajj, showing hospitality towards guests, protecting the property and goods of orphans and taking care of relatives were common among the Arabs before the birth of Islam.
1.3 The Almighty has used many words that derive from the root word of "Hanif" in the Quran and in most verses Allah has commanded the prophet to follow Ibrahim's path; a religion that never underwent distortion and alteration. In some verses it has been stated that Ibrahim's path was a straight and ‘hanif’ one.
In other words in some verses it has been pointed out that Ibrahim was a "Hanif" while in others Allah says that the path he had chosen was a "Hanif" one.
When scrutinizing the verses we find that they do not indicate that there was a specific religion as "Hanifiah", but rather the verses are saying the teachings of Ibrahim should be followed without being altered or changed, and the acts of those who only claim that they follow Ibrahim's teachings but do not practice them in their lives of the Christians, Jews and even sometimes the idol worshippers are not accepted by Islam and the Quran.
At the same time, we all know that the prophets that were sent after Ibrahim like Yaqub, Yusuf, Musa and Isa were descendants and followers of Prophet Ibrahim's path whose teachings were all in line with his, therefore if the books of Musa and Isa were not altered and corrupted they would have been consistent with Ibrahim's teachings. Despite this fact, both Christians and Jews say that they have ‘Abrahamic’ religions!
According to what was explained above one can conclude that there was no organized religion known as "Hanifiah". The Quranic verses that relate to Ibrahim and the ahadith that point out the prophet’s belief in Ibrahim's religion only indicate that the prophet of Islam has always followed the straight path and not strayed from it, like Prophet Ibrahim himself.
2- The question that may come to mind is that if all the holy religions share the same fundamental teachings and that the prophet (pbuh) was supposed to follow the last religion brought to people before him meaning Christianity, then how come the prophet did not publicly announce that he followed those religions? Especially since some of these religions had more followers and were well known. Announcing his faith in Ibrahim and not Jesus or Moses implied that these two prophets of Allah had gone astray and chosen a path other than their ancestor’s!
One may be able to find the answer of such a question by examining what was said above, but in order to explain the answer one more time we will shed light on some points:
2.1 The many religions that were practiced in the Arabian Peninsula had serious differences in beliefs but all shared great respect for Prophet Ibrahim. There is no doubt that all Christians and Jews showed respect for Prophet Ibrahim, but it is very interesting to know that even the idol worshippers revered him. Not only that, but they would also practice some of the rituals that Ibrahim had established at his time like Hajj, and although they had tainted his religion with idolatry and many other wrong beliefs and traditions, they never saw him as their enemy and wouldn’t allow any insulting when it came to him.
2.2 It is easy to forget that even though the prophet publicly told the people that he followed Ibrahim and his teachings, not on one occasion before or after being chosen as a prophet did he oppose the teachings of true Christianity or Judaism, instead Quranic verses indicate that the original teachings of these religions are accepted in Islam.
In other words believing in Ibrahim does not contradict belief in Musa and Isa and from Islam's perspective it is obligatory to follow all of divine prophets, the same way Shias name themselves "the followers of Imam Ali" or the "followers of Imam Sadiq" but actually follow all twelve Imams and obey the commands of all of them.
2.3 Not only did the Prophet claim that he followed Ibrahim before his prophethood but even after being chosen as a prophet, he insisted that he practiced the teachings of this great prophet of Allah. Obviously such a claim does not imply that the prophet didn't consider himself a messenger of Allah and was only a follower of another one. Instead it shows that by following Prophet Ibrahim before his own prophethood, he hadn’t disregarded the prophethood of Musa and Isa and that there were other reasons for him not to say he is of their followers after his prophethood.
2.4 As was explained above, Ibrahim's religion was not practiced by a certain community close to the coming of Islam, and there were no people that considered themselves the preachers or leaders of his religion, however the Christians and Jews had established practicing communities. Christian and Jewish scholars strived to not only cover and hide the alteration they had caused in their religion and preach that religion, but they also made much effort to claim that great people in history like Ibrahim were on their side and practiced their altered religions. For example at the time of the prophet the Jews claimed that Ibrahim was Jewish while Christians would claim that he was Christian. This matter of dispute has been mentioned in the Quran as well. In the Quran Allah reminds the Christians and Jews that Ibrahim lived before the advent of both religions and there was no way he could have been following either one of them, meaning that their disagreements only stemmed from their stubbornness and self-centeredness.
We need to picture what would have happened if the prophet had told the people that he was a follower of Isa. Judging by what they would attribute to Ibrahim as a prophet that lived before both religions, if the prophet of Islam would have said that he followed the Christians or Jews before his prophethood, the Christians and Jews would have always had and excuse to make false claims about his new message and religion.
It seems that problems like this were what didn’t allow the Prophet of Islam to announce his adherence to Great prophets of Allah like Musa and Isa. If the prophet had done such a thing the Christian and Jewish scholars which had actually altered the religion of these prophets could have taken advantage of this and used their many resources to slow him down in fulfilling his mission by inviting him to their religions and in the case of him refusing, to introduce him to the naive people of that time as an apostate who was against their teachings. Finally if they could not stop the prophet from spreading the message of Islam they would still have one more thing to do, and that was to claim that the prophet’s religion was none other than a branch of Christianity or Judaism, not a new religion other than the two.
But by announcing his adherence to prophet Ibrahim, which was in reality an indirect adherence to Musa and Isa, he would not confront these difficulties as well as letting people know that he believed in the previous messengers of Allah.
 Ibn Mandhur, Lisanul-Arab, vol.9 pg. 57.
 "ما کان ابراهیم یهودیا و نصرانیا و لکن حنیفا مسلما و ما کان من المشرکین".
 Kuleini, Muhammad ibn Yaqub, Kafi, vol. 2, pg. 15, hadith 1.
 Sheikh Saduq, Kamaluddin, vol. 1, pg. 199, hadith 43.
 Kuleini, Muhammad Ibn Yaqub, Kafi, vol. 4, pg. 211, hadith 19.
 Baqarah:135; Ale-Imran:95; Nisa:125; An’am:161; Nahl:123.
 Ale-Imran:67; Nahl:120.
 Baqarah:132-133; Yusuf:38.
 Ma’idah:43-47; Shura:13 and other verses.
 Baqarah:136; Ale-Imran:84 “لا نفرق بین احد منهم” and Baqarah:285 “لا نفرق بین احد من رسله”.
 Sheikh Saduq, Kamaluddin, vol. 1, pg. 199, hadith 43.
 Baqarah:140; Ale-Imran:65-67"...یا أهل الکتاب لم تحاجون فی ابراهیم و ما أنزلت التوراة و الإنجیل إلا من بعده أ فلا تعقلون".