Black tea is loaded with tannic acid, and tannins are astringent — they contract tissue and reduce secretion. Applied to feet, that means fewer active sweat glands, and fewer active sweat glands means less of the damp environment athlete's foot needs to survive.
The tannins are also mildly antibacterial, which addresses foot odour directly rather than masking it. This is one of the oldest and best-attested foot remedies there is, and it costs the price of a few tea bags.
Ordinary cheap black tea is what you want here. Green tea has fewer tannins; herbal tea has none.
