What are the fundamentals of religion that one who neglects learning them is considered an apostate, and is neglecting to learn the pillars of prayer, for example, considered apostasy?

In linguistics, i'rad (الإعراض) means turning away from something. As for the i'rad that leads to disbelief (kufr), it is the complete turning away from hearing about the religion, or from examining its proofs, or from learning the fundamental principle by which a person enters Islam, despite being able to do so, or turning away from accepting it and submitting to it wholeheartedly.

Ibn al-Qayyim holds that the kufr of i'rad occurs when one turns away with hearing and heart from the Messenger, neither believing him nor disbelieving him, neither befriending him nor opposing him, and not paying attention to what he brought. Allah Almighty has condemned the disbelievers who turn away from the truth in many verses.

Al-Shanqeeti explains that turning away from the signs of Allah is among the greatest injustices and has severe consequences and repercussions, such as placing coverings over hearts, never being guided, Allah's vengeance, likening the one who turns away to a donkey, the warning of a thunderbolt, a straitened life and blindness, excruciating torment, and having evil companions from among the devils appointed to them.

The most severe type of i'rad that expels one from Islam is turning away from obeying the Messenger, peace be upon him, after hearing his proofs and the clarity of his explanation.

As for the i'rad that occurs from a Muslim, it is not disbelief in itself unless it leads to disbelief. So, whoever turns away from learning the fundamentals of religion that would cause him to fall into disbelief, or denies something definitively known to be part of the religion, or deems permissible something definitively known to be forbidden, he disbelieves thereby. However, whoever turns away from learning something until he neglects an obligation or falls into something forbidden, not deeming it permissible but as a sin, he is considered disobedient by that turning away, and does not disbelieve because of it.

Ibn 'Uthaymeen differentiates between ignorance for which a person is excused and ignorance for which he is not excused. Ignorance resulting from negligence and carelessness is not excused, whereas ignorance in which a person was not negligent and the حرمة (prohibition) of the thing did not cross his mind, he is excused for it.