Islam is the religion of reason and knowledge encouraging its followers to think about every think including their religious beliefs and duties not to accept them without thinking and reflection.
Is it true to say that the capital punishment for the apostate amounts to total ban on any sort of research, thinking and asking questions about the Islamic teachings and doctrines? Or it is not only allowed, but also Muslims are encouraged to question and discuss all relevant matters to the divine religion of Islam.
Jurisprudentially talking all the jurist consults (Maraj'i) in the beginnings of their Islamic rulings' books (Resala Amaliyah) recorded and upheld verdicts according to which it is necessary for all the believers to attain a sufficient level of certainty regarding the fundamentals of their religion. It is evident that without any research, studies, thinking, and questioning such a certainty can not be achieved.
Therefore, asking questions about both the fundamentals and secondary issues of Islamic teachings is permissible for every Muslim on condition that he/she attempts to find the answers consulting and asking the scholars and professionals.
Based on the aforementioned points, it becomes clear that apostate is different from the researcher and Islamic punishment is for the apostate not for the thinkers and researchers. An apostate is the one who discovers the legitimacy of Islam and gains certainty in its truth, but unreasonably turns away from the religion. [Chapter Muhammad: 25]
According to the Holy Qur'an, some groups of Kuffar (nonbelievers) who had discovered truth in Islam, in a flagrant act of jealousy, decided to use different methods to influence believers into turning away from their religion. [Baqarah: 109] They hoped to reach this aim through the circulation of illogical fallacies against Islam. Hence, God, the Almighty, ordered the believers to refrain from the use of violence against the kuffar, but to come forth with logical arguments and reasons in order to battle the propaganda they were spreading. [1] It is important to note that the first and primary divine order given is for the believers to address the followers of other religions in the best of manners, unless they (the nonbelievers) are not in pursuit of the truth but rather aim to oppress and commit injustice against others. [2]
Notes:
[1] Muhammad Baqir Majlisi, Biharul-Anwar, vol. 97, pg. 67, hadith 15.
[2] Ankabut: 46 “و لا تجادلوا اها الکتاب الا بالذی هی احسن الا الذین ظلموا منهم”