All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
There is no doubt that disbelieving in any part of the Quran is an act of disbelief that takes the doer out of the fold of Islam. Mataalib Uli An-Nuha (a Hanbali book) reads in relation to the actions that entail declaring the doer an apostate:
"...or disrespect for the Quran preserved by Allaah, or claiming that it was altered or fabricated, or claiming to have the ability to produce the like of it, or denying its sanctity, all of which constitute acts of disbelief.
Allaah, The Exalted, says (what means):
• {Then do they not reflect upon the Quran? If it had been from [any] other than Allaah, they would have found within it much contradiction.} [Quran 4:82]
• {Say, "If mankind and the jinn gathered in order to produce the like of this Quran, they could not produce the like of it, even if they were to each other assistants."} [Quran 17:88]
• {If We had sent down this Quran upon a mountain, you would have seen it humbled and coming apart from fear of Allaah...} [Quran 59:21]"
Moreover, Fudhayl ibn ʻIyaadh wrote:
"The same ruling applies to the one who denies what has been clearly stated in the Quran after coming to know that it is stated in the Quran preserved in the mus-haf in the hands of Muslims - while he is not ignorant of it (or the relevant ruling) or has not newly converted to Islam - and brings forth as justification for his denial the inauthenticity of the revelation that has reached him, or being unaware of it or the potential confusion on part of the transmitter. Such a person is to be declared a disbeliever for the two above-mentioned reasons, i.e. going against the scholarly consensus and the collectively contiguous reports on the authority of the Prophet . This is because such an act constitutes disbelief in the Quran and the Prophet ." [Ash-Shifa]
Disbelieving in the story of Prophet Ibraaheem (Abraham) when he was thrown into the fire is considered an act of major disbelief because it constitutes disbelief in the Quran. Allaah, The Exalted, says (what means):
• {They said, "Burn him and support your gods - if you are to act." Allaah said, "O fire, be coolness and safety upon Ibrahim."} [Quran 21:68-69]
• {And the answer of Ibrahim’s people was not but that they said, "Kill him or burn him," but Allaah saved him from the fire. Indeed in that are signs for a people who believe.} [Quran 29:24]
• {They said, "Construct for him a furnace and throw him into the burning fire." And they intended for him a plan, but We made them the most debased.} [Quran 37:97-98]
This is the relevant religious ruling in general; however, when it comes to declaring a specific person a disbeliever because of such an act, then he should not be declared so if he is ignorant or the like (of the religious impediments to declaring a specified individual an apostate).
The fact that a given act is considered an act of disbelief does not necessarily mean declaring a specific person who does it a non-Muslim (automatically). Declaring a specific Muslim individual or group as non-Muslim is within the authority of the sharee'ah court or eligible scholars only; please refer to fatwa 14489.
Allaah knows best.