Yes, annoying that they capitalise the L in Libertarian (which is the party not the philosophy) they should keep it lower case when describing a libertarian who is working in the GOP
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.