This is a very broad explanation, and I’m leaving outside lots of detail.
Definition #1 – when you talk about the East coast, don’t include the southern US (Virginia on down) because the South is much more like the middle of the country than it is either the east or west coasts.
Explanation:
The east, in particular, was settled by Europeans (primarily British), and they landed in New England and spread out from there. Because New England has short growing seasons, population spread further west (what became Pennsylvania, Ohio, Indiana) and then further south (Maryland, Virginia, all the way down to Georgia – the thirteen colonies, basically.
New Englanders largely became businessmen, merchants, etc. because they couldn’t earn a living from agriculture, because of the short growing season. So they started universities (Harvard, Yale, Georgetown, and so on) that educated their sons (not daughters at that point). Some families became manufacturers (furniture,, buggy whips, early iron work, milling, etc.).
Meanwhile the South had a LONG growing season, and landowners bought slaves and the South became a huge agricultural center, Cotton, peanuts, corn, anything that they wanted to grow. The South had the advantage of warm weather, as I said, so it could be productive almost all year.
Then gold was discovered in California (which was previously unsettled by whites) in 1849. San Francisco became a mercantile and financial city overnight, practically. It became, in some ways, the New York of the western US. Los Angeles followed a little later. But at that point – 1850s – California was barely settled and populated; business was down in San Francisco but comparatively little agriculture. That started seriously after the civil war.
Meanwhile, the midwest and central plains areas grew as the population grew and looked for opportunities outside of New England. Chicago, Cleveland, Pittsburgh, later Omaha, Kansas City, Denver, etc., helped along by the railroad, became major merchant cities of their own.
Because of the huge expanses of land throughout the US, the whole central area because a massive agriculture heaven – crops of all types were grown, and cattle, pork, and poultry leveraged the land to feed the rest of the country.
So back to your question:
1) first, the republicans during the civil war era (1850–1865) were considered the liberals and free thinkers, and the democrats were considered the conservative party. Keep in mind that Abe Lincoln was a republican. That all changed in the last 150 years.
2) Agriculture is by nature a conservative function – it takes advantage of the land and is comparatively a slow process (it takes 4 months to raise corn). You didn’t need much of an education to be a successful farmer. (And until about 40 years ago, that remained true). Advances in growing have taken place, but nowhere near at the rate of manufacturing or commerce.
3) Manufacturing: cars, tractors, trains, bulldozers, and a zillion other things – took advantage of creative and educated people that largely lived in (or had come from) either New England / NY or from California (Stanford University, for example, trained a lot of technologies 100 years ago).
Business and mercantilism by nature is a faster process than agriculture. Products are invented in weeks, not the two years it takes to raise a calf.
conclusion: The east and west coast attracted people who were (are) liberal and aggressive thinkers. Problem solvers. That aggressiveness translate into aggressive and liberal politics.
The slower-paced agricultural antecedents of the midwest and south have generally led to a less aggressive, more conservative outlook.