Why do we object to Christians anointing themselves with statues and sanctifying images that they claim secrete oil, while some Muslims wish to touch and kiss the Kaaba, and others broadcast live videos of rain in the Haram, even though rain is a natural phenomenon that occurs everywhere?

It is prescribed for a Muslim to kiss the Black Stone alone, in emulation of the Prophet, peace and blessings be upon him, not seeking benefit or warding off harm. This is an act of complying with Allah's command, seeking His reward. This differs from seeking blessings from images to gain benefit and ward off harm, which approaches polytheism. As for photographing rain in the Haram, it is a custom, not an act of worship. Whoever believes it to be a supernatural phenomenon is ignorant, and this is completely different from someone who believes that a static image secretes blessed oil as proof of the validity of their worship of other than Allah.