Apostasy is defined as “The state of having rejected your affiliation, religious or political beliefs, or principles (often in favour of opposing beliefs or causes)” (WordWeb).
Buddhism encourages a sceptical attitude, and does not demand blind faith. One becomes a Buddhist by the simple act of taking refuge in the Buddha, Dhamma, and Saṅgha, which is an expression of one’s confidence in the teachings. One becomes a virtuous Buddhist by undertaking and observing the five precepts (abstaining from killing living beings, stealing, sexual misconduct, wrong speech, and taking intoxicants that cause heedlessness).
There are many followers of Buddhism who do not have full confidence in orthodox doctrines such as the law of kamma and rebirth, psychic powers, mind-reading, the existence of other realms of existence, etc. These core beliefs are elements of mundane right-view. However, being sceptical about these beliefs does not make anyone an apostate.
An apostate is someone like the monk Sunakkhatta who was angry with the Buddha, and left the Saṅgha.
By his own misdirected mind, Sunakkhatta set himself on a course that would inevitably lead to rebirth in hell. The Buddha did not inflict any punishment on him, Sunakkhatta’s path was one that he chose for himself. This is what the Maha-sihanada Sutta says regarding Sunakkhatta:
21. “Sariputta, when I know and see thus, should anyone say of me: ‘The recluse Gotama does not have any superhuman states, any distinction in knowledge and vision worthy of the noble ones. The recluse Gotama teaches a Dhamma (merely) hammered out by reasoning, following his own line of inquiry as it occurs to him’ — unless he abandons that assertion and that state of mind and relinquishes that view, then as (surely as if he had been) carried off and put there he will wind up in hell.
Just as a bhikkhu possessed of virtue, concentration and wisdom would here and now enjoy final knowledge, so it will happen in this case, I say, that unless he abandons that assertion and that state of mind and relinquishes that view, then as (surely as if he had been) carried off and put there he will wind up in hell.
No Buddhist worthy of the name would want to kill or punish an apostate. They might want to reason with them to restore their faith, or they might ostracise them if they refused to listen to wise counsel.
See the Kesi Sutta. to understand the Buddhist attitude to apostates and others who adhere to wrong-views and engage in misdeeds.