Does the mere occurrence of intrusive thoughts affect faith or defile clothing and food? And is one required to spit with every intrusive thought, especially in public places? And how can one reconcile ignoring intrusive thoughts with seeking refuge from them?

The meaning of your question about the effect of intrusive thoughts and their consequences, and whether they diminish faith, was not understood.

The Prophet, peace and blessings be upon him, commanded seeking refuge [with Allah] and spitting lightly to the left three times upon feeling intrusive thoughts. It is narrated in Sahih Muslim that Uthman ibn Abi al-Aas complained to the Prophet, peace and blessings be upon him, about the devil's intrusive thoughts during his prayer. So, he commanded him to seek refuge with Allah from it and to spit lightly to his left three times. He did so, and Allah removed the intrusive thoughts from him.

The hadith does not specify a number of repetitions; rather, it is done whenever intrusive thoughts occur. The combination of seeking refuge and turning away from intrusive thoughts is what is required, by seeking refuge and then turning away from them and not dwelling on them.