All praise is due to Allah, and peace and blessings be upon the Messenger of Allah.
No. This claim has no sound rational or Islamic basis. The presence of birds above the Kaaba or the falling of bird droppings on it does not diminish the honor of the Kaaba, nor does it contradict Allah's protection of His Sacred House. Allah governs the universe according to His established laws and has not made protecting the Kaaba mean preventing every natural phenomenon from occurring around it.
The Kaaba is a building that Allah has honored and made the direction of prayer (qiblah) for Muslims. However, it remains part of this world and is subject to the natural laws established by Allah. Rain falls upon it, winds blow around it, it is washed, and it is regularly cleaned. None of this reduces its sanctity or status.
Moreover, according to the majority of Islamic scholars, the droppings of many birds living in the Sacred Mosque are considered ritually pure, so their presence does not create any Islamic legal issue.
This argument is based on a false premise. The real question is not, "Can birds fly over the Kaaba?" Rather, it is: "Does this prove that Islam is false or that Allah does not exist?" The answer is clearly no. There is no logical connection between the two.
Allah's power does not mean that He prevents every natural occurrence. Rather, He does whatever He wills with perfect wisdom. At times, He protects His Sacred House through miracles when wisdom requires it, as happened in the incident of the People of the Elephant, while at other times He allows events to proceed according to His usual laws.
Therefore, this claim is nothing more than an attempt to provoke ridicule. It provides no evidence whatsoever against Islam or its beliefs.
And Allah knows best.