Classical liberalism is a political ideology, a branch of liberalism which advocates civil liberties and political freedom with limited government under the rule of law and generally promotes a laissez-faire economic policy.
Sounds good to me. The social conservatives have nothing to fear from a Classical Liberal. Such a person has a biblical definition of good and evil and will side with good. Abortion and same sex marriage are evil.
Classic liberalism, ie. John Locke and Thomas Jefferson, is the ideology America was founded on. The conservatives of the day were Tories, who wanted to "conserve" monarchy and state religion. They left after the revolution. So in America "the right" is conserving classic liberalism. While in Europe "the right" includes a strong streak of statism. That's why fascism is considered to be on "the right", even though it is totally opposed to American conservative values.