Is it permissible to describe one who entirely abandons prayer, or some prayers, as a disbeliever (kafir)? And is it permissible to return his greeting of peace and interact with him? And what are the proofs from the Qur’an and Sunnah that allow or prohibit that?

Abandoning prayer is one of the gravest sins. One who abandons it is described as a disbeliever (kafir), but the majority of scholars hold that this disbelief does not expel one from the fold of Islam. It is not permissible to address one who abandons prayer as a disbeliever (kafir) because the term "kufr" (disbelief) typically refers to disbelief that expels one from the fold of Islam, and also because such an address would alienate them. They should be addressed with wisdom and good counsel, and reminded of the stern warnings against those who abandon prayer without directly applying them to the individual, and with words that win over their heart. It is permissible to conduct transactions with them, buying and selling, taking and giving. It is permissible to eat their food and accept their gifts. It is permissible to return their greeting of peace and to initiate it with them, because they are Muslims. However, some scholars have preferred to refrain from doing so as a deterrent, provided that such shunning would be more beneficial for them.