Making abatch of Feta, Mozzarella, and riccotta using the leftover whey from the Feta and Mozzarella as we speak (er, type. And that's the royal we, unless you happen to be typing at the same time as I am

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I make the cheese in the kitchen, and for the most part my brewing is in the garage until the beer is in the fermenter, then I bring it in and oxygenate and pitch my starter in the kitchen.
There's lacto everywhere in the kitchen. If you are making clean beer, and practice good sanitation, I don't think you have to worry about cheese. I'm more worried when I bake bread because flour floats, milk doesn't.
As far as aging cheese in your kegerator ..... why not? Your beer is safely protected in a positive pressure vessel. Keep your cheese in a tupperware container so you don't leak whey you should be fine. Wipe things down periodically with StarSan if you are worried!