Is there a problem having both kinds of food in the fridge? You have to assert yourself when it comes to having your kinds of foods available. Is he trying to restrict your eating also?
If this is just an issue of different dietary habits, well, when we got together I was a vegetarian and RAH was a chef and dedicated meat eater, a snout-to-tail type that grossed me out to high heavens. Today, we eat veggie some days (most days in the summer) and meat on other days, but we also have "fend for yourself night" several nights a week.
If this is bothering you because it's triggering for you, because it's obsessive, because it's a sign of tetchy mental health, it's a dealbreaker and you need to treat it as such.
He's grown, he can choose whether or not to pursue this lifestyle. Admittedly, some mainstream weight loss and maintenance plans are pretty extreme. But personally, I couldn't live with a person who ate such a restrictive diet, like a paleo diet or a vegan diet for example. It would get annoying to me, for one, and for two, it's just a different way of living that I'm not willing to adhere to. You don't have to either. Incompatible is incompatible.