Highly antimicrobial dairy products, and especially highly antimicrobial fresh cheese products, that are resistant to growth of both Gram positive and Gram negative pathogens are provided. Remarkably, these products are resistant to all five major pathogens that commonly present contamination problems in fresh cheese. The products are prepared by acidifying a dairy product to a pH of 4.5 to 6.1 with an inorganic acidulant and then incorporating an antimicrobial composition containing a bacteriocin and an antimicrobial organic acid. Methods of retaining desired functional characteristics in such antimicrobial dairy products are also provided.