I like the word "liberal" and am very comfortable with the word "classical" in front of it. Many American conservatives are liberals in the deepest sense - they back the free market, the First Amendment, the broad balance of the American constitution, a decent respect for the opinion of mankind. But what has emerged in recent years is a darker, more authoritarian strain of conservatism - rooted in the cultural and racial conservatism of the South, partial to a near-dictatorial war-presidency, believing in American exceptionalism to the extent that it exempts America from the moral norms of the rest of the world, and rooting the legitimacy of the American constitution in only one religious tradition (narrowly defined).
These characters want to redefine conservatism around this theocratic, authoritarian, self-justifying ideology. I am more than happy to share the term liberalism with others. I am not going to have the word conservative coopted solely by these religious radicals.