If jinn enter and exit a person through the Qur’an, then how is their entry and exit among Jews and Christians explained, given their distorted scriptures, along with the observed screaming and flailing of those afflicted among them?

The fact that the books of the Jews and Christians are distorted does not prevent jinn from leaving through their incantations, either because their incantations are polytheistic, or because they contain some truth that remains in their books. Abu Bakr and Aisha instructed those who perform incantations to do so with the Book of Allah. There is no harm in incantations as long as they do not involve shirk (polytheism), even the incantation of a disbeliever for a Muslim is permissible if it is free from shirk. It is not a condition for incantations to be solely with narrated phrases or the Quran; the incantations of non-Muslims may also be effective due to their validity or their seeking assistance from jinn. Describing legitimate reciters as charlatans is a mistake and an injustice to the righteous among them.