It takes a certain type of person to look at a Rothko painting --
-- and see great art.
(Basically, the same type of person who can look at biological gender and see a social construct.)
The modern art dichotomy, in terms of how it reveals political leanings, is thus easy to understand. You're either the type to think the emperor's new clothes are beautiful, or you aren't.
Food is a different matter. It's harder to understand why political opinions should fall along nutritional lines. But, they do, although the lines are a little blurrier than they are with modern art. People's eating habits usually reflect their politics.
Liberals tend to believe in the food pyramid, which emphasizes carbs over protein. Conservatives are more likely to believe in the paleo or zone diets, which tend to emphasize protein over carbs. A poll taken at a pasta restaurant would favor Hillary; at a steakhouse, Trump.
If you see someone eat an entire meal (either breakfast, lunch, or dinner, not just a snack) with no protein, or only a tiny bit of protein (say, the cheese on spinach pie), that person is more likely to be a liberal.
Liberals prefer organic food. Conservatives tend to be indifferent to the presence of pesticides, though more conservatives have switched to organic recently.
Liberals tend to hate genetically modified foods ("Frankenfoods"). Never mind that the molecular composition of these foods is similar and there's never been a single person harmed by eating them. Liberals tend to believe that eating these is basically the equivalent of filling your bathtub with Chernobyl wastewater.
Liberals are more likely to cut fats and salt from their diet. Conservatives, sugar.
Liberals are more likely to prefer sharp (smelly) cheeses. Conservatives are more likely to be happy with Swiss cheese or American brands.
If food is used as a way to show one's sophistication or signal status, you're likely dealing with a liberal. Liberals gravitate toward more pretentious, preferably foreign, foods. And they're more likely to be foodies, period.
In 2014 Gwyneth Paltrow held a Democratic fundraiser at her house attended by Barack Obama; she also has said, "I'd rather smoke crack than eat cheese from a tin." Coincidence? (I think not.)
Liberals are more likely to wash their food down with locally brewed, artisanal beers, which they insist are superior. (Any time you find yourself wanting nothing more than to give someone a blind taste test, you're probably dealing with a liberal.)
In some ways, it's easy to see the correlation with certain kinds of pretensions and political correctness (which is simply another kind). But in other cases, it's harder: why would liberals lean more toward carbs and conservatives toward meat?
I can't figure it out.