Does a person commit an act of disbelief (kufr) if he greets someone who does not pray?

One does not disbelieve by greeting a person who abandons prayer, because the majority of jurists do not consider him a disbeliever unless he denies its obligation. However, it is forbidden to initiate a greeting with a disbeliever, based on the Prophet, peace and blessings be upon him, saying: "Do not initiate greeting the Jews and Christians."