How can one refute the specious argument of the disbelievers that the Prophet (peace be upon him) was a racist when he said that the Caliph must be from Quraish?

The caliphate being among the Quraysh is due to divine wisdom. Allah chose Quraysh from Kinana, and from Quraysh He chose Banu Hashim, and from Banu Hashim He chose the Prophet, peace and blessings be upon him. This means that Quraysh are a source of goodness, and they were distinguished by their noble strength and sound judgment. For example, a Caliph from Quraysh possesses the strength of a man not from Quraysh, but this is conditional upon their adherence to the Sharia and justice. If the Caliph does not uphold the law of Allah, he is to be removed, whether he is from Quraysh or not.