I had always thought that blue cheeses made with Penicillium roqueforti, Penicillium camemberti, and Penicillium glaucum had at least some antibiotic effect, but Google searches say otherwise:

 

https://www.sciencedirect.com/science/article/pii/S0022030254913880

 

My question is are there any cheeses that do have antibiotic activity?

Sorry, no antibiotic cheeses, in fact you don't want antibiotics in cheese as they could prevent the fermentive bacteria from doing their job.  Same with yogurts - the probiotic cultures need to thrive, being bacteria that help you digest that food.

Some herbs and spices are somewhat antibiotic, like ginger or turmeric or garlic, and they don't bother the good gut bacteria.  Apple cider vinegar is also a good one (and also reduces phytates in foods, which then improves zinc absorption and thus can boost immune response).  Oregano is antifungal.  

IOW, eat lots of curry and Italian!  😀

Antibiotics are indiscriminate killers of anything that is sensitive to them. Target nutrients or the good guys and they'll reduce the habitat possibilities for the bad ones