The “left…right” is just not a good scale, it only refers to where people sit. In reality there are several orthogonal scales, like:
Conservative — Progressive
Totalitarian — Anarchist
Nationalist — Internationalist
Capitalist — Communist
Autocrat — Democrat
Monarchist — Republican
Bigoted — Egalitarian
…and some more.
That means there can be “Conservative Anarchist Bigots”, and “Progressive Capitalist Bigots”, and “Progressive Anarchist Internationalist Communist Democratic Republican Egalitarians” (sometimes called “hippies”), or “Monarchic Democratic Internationalists” (we have some of those in Spain). The scales don’t really influence each other (“Autocratic Monarchist Anarchists” are rare nowadays, but they do exist and have a precedent in Aristotle’s “one good ruler” idea, or the “Benevolent dictator for life” in FOSS).
China right now, is a “Conservative Totalitarian Nationalist Capitalist Autocratic Bigoted Republic”, they only keep “Communist” in the name for historical reasons, and to prevent anyone from trying to push for actual communism. To their credit, they’re still “Popular” (Nationalist) and a “Republic”… yet it’s still anyone’s guess when they might become a “Hereditary Autocracy” (aka: Autocratic Monarchy) like North Korea.
What I find the funniest though, is US’s “Democrats vs. Republicans”… they’re not even on the same scale! While the country is already both, a “Democratic Republic”, the parties are named less like what they might defend, and more like an insult to each other: “you’re a monarchist!” vs. “you’re an autocrat!”. And look at that, a Republican wannabe-Autocrat is getting indicted right now… but might still win the Democratic elections 🤦