Is there no contradiction between the obligation to divorce a Muslim woman who does not pray and the permissibility of marrying a Kitabiyah (People of the Book) who does not pray?

There is no flaw in the fatwa. Rather, the flaw came from the questioner's desire to equate a Muslim woman who abandons prayer with a Jewish or Christian woman. This is incorrect because abandoning prayer is major disbelief (kufr akbar) and apostasy (riddah). The ruling on an apostate is stricter than that on an original disbeliever. Therefore, their slaughtered animal is not permissible to eat, and it is not permissible for a Muslim to marry them. If the wife apostatizes, the marriage is annulled.

The madhhab of Imam Ahmad and some scholars is that one who abandons prayer is a disbeliever. Thus, they forbid marriage to one who does not pray and obligate separation from her if she abandons prayer. This is what we have followed in related fatwas.

Similarly, if a woman commits an act of disbelief, such as insulting Allah or His Messenger (peace be upon him) and insists on it, it is not permissible for her to remain a Muslim's wife. Likewise, if a husband is ruled to have apostatized, separation between him and his wife is obligatory.