All Muslims follow the religion of Ibraaheem (blessings and peace of Allah be upon him)
Question

Is it permissible for me to say that I follow the religion of Ibraaheem, because it does not differ from Islam?
Praise be to Allah.For a Muslim to say “I follow the religion of Ibraaheem (blessings and peace of Allah be upon him)” is a fundamental teaching of Islam. Allah, may He be exalted, says (interpretation of the meaning):
{And who would be averse to the religion of Abraham except one who makes a fool of himself?} [al-Baqarah 2:130]
{Say, Allah has told the truth. So follow the religion of Abraham, inclining toward truth; and he was not of the polytheists} [Aal ‘Imraan 3:130]
{And who is better in religion than one who submits himself to Allah while being a doer of good and follows the religion of Abraham, inclining toward truth? And Allah took Abraham as an intimate friend} [an-Nisa’ 4:125].
Imam Ahmad (21144) narrated that Ubayy Ibn Ka‘b  said: The Messenger of Allah (blessings and peace of Allah be upon him) used to teach us to say when morning came: “Asbahna ‘ala fitrat il-Islam wa kalimat il-ikhlaas wa sunnati nabiyyina Muhammad sall-Allahu ‘alayhi wa sallim wa millati abeena Ibraaheema haneefan musliman wa maa kaana min al-mushrikeen (This morning we affirm our adherence to the path of Islam and the word of sincerity and the way of our Prophet Muhammad (peace and blessings of Allah be upon him) and the religion of our father Ibraaheem, pure monotheism and submission to Allah, and he was not of those who associate others with Allah).” And when evening came, we were to say something similar.
Classed as saheeh by al-Albaani in as-Saheehah (2989).
Shaykh Muhammad ibn ‘Abd al-Wahhaab (may Allah have mercy on him) said:
You should understand, may Allah guide you to obey Him, that al-haneefiyyah (monotheism) is the religion of Ibraaheem. It means to worship Allah alone, with sincere devotion to Him. This is what Allah has enjoined upon all people, and He created them for that purpose, as He, may He be exalted, says (interpretation of the meaning):
{And I did not create the jinn and mankind except to worship Me} [adh-Dhaariyaat 51:56]." (Thalaathat al-Usool  p. 8).
Shaykh ash-Shinqeeti (may Allah have mercy on him) said:
The words of Allah (interpretation of the meaning), {And who would be averse to the religion of Abraham …?} [al-Baqarah 2:130], do not explain what the religion of Ibraaheem is, but elsewhere He explains that when He says (interpretation of the meaning):
{Say, “Indeed, my Lord has guided me to a straight path - a correct religion - the way of Abraham, inclining toward truth. And he was not among those who associated others with Allah} [al-An‘aam 6:161].
In this verse, Allah clearly states that it is the religion of Islam, with which He sent His Prophet Muhammad (blessings and peace of Allah be upon him). And He said something similar in the verse (interpretation of the meaning):
{Then We revealed to you, [O Muhammad], to follow the religion of Abraham} [an-Nahl 16:123]." (Adwa’ al-Bayaan  1/44).
Thus the religion of Ibraaheem is affirmation of the oneness of Allah (Tawheed), disbelief in whatever is worshipped besides Him, and submission to Him, may He be glorified, with regard to His rulings and laws.
If someone says that the religion of Ibraaheem is no different from Islam, if what he means by that is that it does not differ from Islam because it is Islam, then yes, that is correct.
But if he means that it is something other than Islam, but that it does not differ from Islam in its essence, then no, that is not correct. What knowledge does he have of the religion of Ibraaheem, except what Islam tells us?
Moreover, if anyone claims to be following the religion of Ibraaheem, as noted above, that can only be done by following Islam and being Muslim, but if someone were to stop following Islam for some reason or another, on the grounds that he is following the religion of Ibraaheem, that is not wrong and is not acceptable. Allah, may He be exalted, says (interpretation of the meaning):
{O you who have believed, bow and prostrate and worship your Lord and do good - that you may succeed.
And strive for Allah with the striving due to Him. He has chosen you and has not placed upon you in the religion any difficulty. [It is] the religion of your father, Abraham. Allah named you "Muslims" before [in former scriptures] and in this [revelation] that the Messenger may be a witness over you and you may be witnesses over the people. So establish prayer and give zakah and hold fast to Allah. He is your protector; and excellent is the protector, and excellent is the helper} [al-Hajj 22:77-78].
Please see also the answer to question no. 145516 .
And Allah knows best.