I think a lot of the party emphasis in the US is a consequence of first-past-the-post elections for every position.
So rather than build coalitions of smaller parties centered around certain interests, you end up with two parties who broadly represent the two sides of the spectrum. The Democrats are the US’s left wing, with an emphasis on more progressive policies, equality, and social justice. The Republicans are the US’s right wing, with a traditional emphasis on the status quo, pro-business policies, and a strong military.
One major sticking point between the parties that causes friction is the perceived role of the government. The Republicans tend to have the belief that it’s a necessary evil at the best of times, and that strong efforts to rein it in and prevent it from sticking its tendrils into the business of the commercial world and people’s personal lives are necessary. Democrats view the government as the single biggest agent for change- the government has the money and the legitimate power to make stuff happen. As you can imagine, these two are rarely compatible- each side sees the other as deliberately working against their agendas.
Now all that above was probably more or less true through the late 1990s. Then something weird happened to the Republican party, which AFAIK was the “Contract with America” and increased party discipline combined with (loony) far-right elements like the Tea Party taking the party by the short and curlies and taking everything to the insane extreme. Rather than seeking to limit the expansion of government and maintain the status quo, these elements actively seek to roll back the clock in a lot of ways. Combine that with the fact that most of them are fairly ignorant and wistfully reminisce about a past that either never was, or was the product of a specific time and place, and think that it was the normal state of things, rather than a historical aberration due to the US’s post WWII economic position. They literally don’t realize that no amount of political shenanigans or policy will bring that back- too many other countries can manufacture stuff of reasonable quality and cheaper than we can. Or that coal mining as a going concern has its days numbered due to environmental and economic forces, for example.
There’s also a real friction point between the Democrats and Republicans on what I’d call the battle between compassion and order/responsibility. The Democrats tend toward a compassion-driven public policy and platform- their usual MO is that when push comes to shove, compassion wins out over strict adherence to the laws or fiscal responsibility, especially on immigration or other social issues. Basically they’d rather make someone’s life better than worry about budgets or the law. A lot of the Republican types are the opposite- they don’t see undocumented immigrants who need help, they see illegal aliens who are breaking our laws and driving wages down.
I guess to me, the biggest issue is that the Republicans have let the inmates start running the asylum- the moderates and middle-right aren’t running the party; they’re typically called RINOs (“Republicans In Name Only”) because they’re not so far to the right as the others. Instead, the far, far right types are now running things. Trump is more of a symptom of that than a cause, for example.