I'm pretty sure both sides stereotype the other. You can say this article about the racist and fundamentalist components of Trumpism is just another stereotype. I'd agree it's not the whole truth of conservatism. But I wrote a long series on conservatism, the links to which you can find in the article below. I don't respect what's called social conservatism or laissez-faire/neoclassical/neoliberal economics.
But these terms are so elastic. For instance, I think you have a valid point against the neoliberal ideology of free trade, which Bill Clinton and the subsequent DNC promoted. Is free trade a "liberal" policy though? Ronald Reagan is the one who pushed it through after the stagflation crisis ended the Keynesian consensus. That debate goes back to the Gilded Age, the Progressive Era, the Great Depression, and the New Deal.
The key distinction, I think, is between those who like capitalism more than republican government, and those who think a strong government is needed to curb the excesses of capitalism. That's the upshot of the split between so-called modern conservatives and liberals. The former's libertarian view amounts to social Darwinism, and the latter's view points towards socialism or secular humanism.
