Yes. Classical liberalism was a well understood notion when America declared its independence and defeated the most powerful Empire on the planet at the time. An American conservative is a person who still believes all those things. Thus American conservatives are European classical liberals. They would cheer on the president taking months of his time to make sure an edition of the Holy Bible is available to be used by the federal government to convert native peoples to Christianity: just like Thomas Jefferson actually did. No one should (or did) find this at all strange.

There were always two poles of US political debate, but their squabbles were small. It was often about coinage or how quickly to end slavery (yes, end. None in power actually thought it would go on forever). But after, say 1885 contact with Europe introduced an entirely foreign political pole: Leftism. Within a generation suffragettes would form the first 'coalitions' in this new ideology that increasingly left the previous consensus of US conservationism in the dust. They called themselves liberals and conservatives didn't fight the labeling.

Then came Socialism, FDR and the Civil Rights acts (which allow Trans to sue for gender discrimination now by the way, thanks to the Supreme Court). Race riots, skyrocketing divorce, criminalizing self defense, it all came be seen in infantile forms if you trace the history back far enough. That's why "liberalism" as two different uses but Leftist and Conservative don't. Something similar happened with the Red vs Blue coloring in the 1970s with the big 3 Mainstream Media outlets deciding to just swap whether Democrats were Reds or not. They didn't like voters realizing Democrats and Socialists/Communists shared the same color. That was considered a slur or something that needed to be hidden. You know, standard 1984 double-think.