This is a hard question to answer, but I'll take a stab at it.
First, to my knowledge there is no culinary term for this. ("Savory-except-for-dessert-ovore"?) There's also no "style of food" that seems explicitly dedicated to maintaining a strict "savory-except-for-dessert" philosophy, though there certainly is a trend in traditional American and some European cuisines to keep such flavors separate with only specific exceptions. (For example, the raisins in stuffing and cranberry sauce with turkey combinations of sweet and savory are a few classic exceptions in American cuisine.)
Most of this comes from cultural associations about "appropriate" flavor pairings. We all have oddly specific associations with flavors and food often shaped an early age, as well as specific ideas about "what goes together." It's not only sugar with desserts, but also specific spices associated with dessert -- in America and parts of Europe, cinnamon is associated with sweet foods, but in Asian and the Middle East, cinnamon is often put in meat dishes. I know many people who find the latter pairing to be weird or bizarre.
For another example, why are certain foods considered appropriate "breakfast foods," while others are not? Most Americans would think having a hamburger or chili for breakfast to be a bit weird, but take a different meat (pork), mix in appropriate "breakfast spices" and fry it up, and you have an appropriate "breakfast sausage." And combining breakfast foods with other foods is often thought to be bizarre, but why can't you order a hamburger with cereal on the side instead of fries and a shake (also a combination of starch and dairy)? Why can't you eat pancakes with chili?
Even the most adventurous people who'd call themselves "foodies" would probably balk at some point here -- and often not for any good reason other than we just don't do that.
Anyhow, there is a trend in recent years to incorporate more "adventurous" sweet and savory combinations: herbed sweet cakes, meat with fruit chutneys, bacon ice cream, etc. A lot of these dishes have historical roots, but they seem to be becoming more popular.
Does it make you "unsophisticated" if you don't like such things? I personally would never say so (though I also wouldn't personally call myself a "foodie," for whatever that's worth). Our taste preferences are often deeply culturally engrained, and I suppose some people view those who unwilling to try new flavor pairings as old-fashioned boring "meat-and-potatoes" eaters.
But in reality the traditional Anglo-American division with sweet reserved for dessert (with circumscribed exceptions) makes a certain amount of sense. Meat and vegetables tend to have strong flavors on their own, as do sweet ingredients (sugar, honey, syrup, and even many fruits). Desserts often combine these latter sweet ingredients with blander foods like flour and eggs, thereby enhancing the bland ingredients and diluting the sweetness to something palatable. Thus, separating these ingredients allows one to experience maximum strong meaty/vegetal flavors and later a maximum strong sweet flavor, allowing separate appreciation of these contrasts.
But of course that's only one possible culinary aesthetic, and the current trend seems to have sweet and savory coming together in more ways. To my knowledge, there hasn't been a strong enough backlash against this to come up with an individual term for those who don't like it, though.