Are the Kaaba and the Black Stone considered idols because they neither move nor benefit, by analogy with Islam's destruction of idols in the pre-Islamic era (Jahiliyyah)?

This misconception is refutable. Allah chose Makkah and made the Kaaba the Qibla for Muslims in their prayers. He commanded Muslims to perform Hajj to this House and to circumambulate it, in glorification of Allah the Almighty, because it is among the rituals of Allah: "That [is so]. And whoever honors the symbols of Allah - indeed, it is from the piety of hearts." (Surat Al-Hajj, 32). The circumambulation of the Kaaba by Muslims and their facing the House in their prayers is a glorification of the rituals of Allah the Almighty. They do it in obedience to Him and in compliance with His command, knowing that the Kaaba and all creatures possess neither harm nor benefit. Similarly, their veneration of the Black Stone and their kissing it during their circumambulation is merely following the Sunnah of the Prophet, peace and blessings be upon him, and it is not an act of worship to the stone. The Commander of the Faithful, Umar, may Allah be pleased with him, said: "By Allah, I am kissing you, and I know that you are a stone and that you neither harm nor benefit. Had I not seen the Messenger of Allah, peace and blessings be upon him, kiss you, I would not have kissed you."