Discovered by Alexander Fleming in 1928, the antibiotic properties of penicillin, derived from a species of Penicillium fungus, are still widely used today, though many bacteria have become resistant to the drug over time.
Antibiotic resistance occurs when bacteria are regularly exposed to doses of antibiotic that are not quite strong enough to kill all the bacteria. In these situations, the antibiotics only kill off the weakest bacteria, which leaves the slightly stronger ones to multiply and spread their more resistant genes.
Blue cheese does contain cultures of Penicillium mould. You might therefore think that eating too much blue cheese could have a similar effect to antibiotic resistance, by overexposing the bacteria in your body to Penicillium.
However, the strains of Penicillium that are used in cheesemaking are different to the ones in the drug, and don’t have any significant antibiotic properties to begin with. Besides, they are destroyed by your stomach acid anyway.