What is the ruling on one who believes in the Qur’an and the Sunnah and all Hadith, with the exception of the Hadith of "killing the gecko," due to what is mentioned therein about the gecko blowing fire on Abraham, while believing in the necessity of killing it only for harm?

The reason for killing the gecko is that it is harmful and damaging. In addition to that, its species is inherently evil and corrupt. Belief in this matter is a branch of affirming that the Prophet, peace and blessings be upon him, said it. So, whoever believes in the authenticity of this from the Prophet is obliged to believe in it. As for one who doubts its authenticity and rejects it, that does not contradict his faith. A Muslim must accept a hadith (definition) that meets the conditions of authenticity, especially if it is authentically reported in the Two Sahihs (Bukhari and Muslim).