Is saying "What does that mean?" upon hearing some people's lineage attributed to the tribe of the Prophet, peace and blessings be upon him, considered a diminishment for which a person disbelieves and necessitates his killing even after repentance? And what is the ruling on similar thoughts that may cross a person's mind?

The Fatwa's Summary:

You must completely disregard obsessions and not succumb to them, for obsession is an ailment whose cure is complete avoidance. This remedy has been tried by those who were successful, and it worked for them. As for whoever listens to obsessions and acts upon them, they will continue to escalate until they drive him to the brink of insanity. It has been authentically reported in the Sahihayn that whoever is afflicted by obsession should seek refuge in Allah and desist. Obsession comes from Satan, and his sole aim is to plunge the believer into the abyss of misguidance and confusion. Al-Izz ibn Abd al-Salam and others have stated that the cure for obsession is for the obsessed person to believe that it is a satanic thought, and that Iblis is the one who instilled it in him, and that he is fighting him. In doing so, he will receive the reward of a mujahid, because he is fighting the enemy of Allah.