Almost. What you'd call "conservatism" is just slowed-down progressivism, delayed by 10-20 years but otherwise indistinguishable, and both "sides" are squarely within the liberal political theory.
Nothing is being conserved. Today's conservatives are espousing values that sound the same as 2005's liberals, and are not even as conservative as Bill Clinton.
... as a result of decades of clear harms, demonstrated in court cases establishing case law that eventually becomes codified through legislation. The "conservative" values you mention are in fact regressive, and so-called classical liberalism is centrist, not progressive.
Nothing is being conserved. Today's conservatives are espousing values that sound the same as 2005's liberals, and are not even as conservative as Bill Clinton.