I'm European, I know this very well. And still, the absolutist/dictatorial streak in Donald Trump's philosophy of government is something that XIX century liberals would simply abhor. He doesn't believe in consent (and not just "of the governed"), he doesn't believe in individual rights beyond his own... Even just his successful legal moves to obtain full immunity is the exact opposite of "equality before the law".

(I also disagree that the two US parties share "a certain set of beliefs". This might have been true 15 years ago, but after the Trump takeover it's becoming increasingly difficult to see any common principles between any other party and what is effectively a satrapy.)

George W. Bush's administration already showed a streak for dictatorial rule that had nothing to do with classic liberalism; Trump took that to extremes. Classic liberalism developed in opposition to absolutist monarchies, promoting rule by parliament - Bush and Trump did the exact opposite. They are not classic liberals by any stretch.