An interesting observation to me is that some confuse libertarian conservatism with (classical) liberalism. There are some profound differences that may be easily overlooked.
A classical liberal seeks individual liberty, economic freedom, a small government and rule of law. These components are shared with social liberalism and in some degree conservative liberalism. However, it does not mean implicitly demanding other individuals to be similar to oneself. A liberal loves differences. It is a privilege to be different from somebody else, not similar. Of course, similarities are welcome, but they are not a condition to live in the same society.
Whereas the libertarian conservative cares about individual liberty, it is a concept of individual liberty that conforms to her/his sense of reality. It is a sense of liberty that confines itself to the primary individual and is not concerned about other individuals. It does not mean social justice has to be included in every school of liberalism, but this does mean that it rejects value pluralism. A component that is significant to liberalism, but hardly accepted in schools of conservatism. This makes a libertarian conservative in core a conservative, and not a liberal.
Why is this so important to realize? Well, if libertarian conservatism is considered to be a subset of liberalism, it opens a window of opportunity to seek those who conform to the values of some branch of libertarian conservatism and does not promote the diversity of values. A Christian may be a Christian, a Jew may be a Jew, a Muslim may be a Muslim, and and Atheist may be an Atheist. A painter is a painter, a scientist a scientist and an economist an economist. There should only be an individual distinction with them, without projection of certain values or prejudices.
Liberalism is not solely about “live and let live”, it’s about “live without infringing on the lives of others”. Most schools of liberalism would not violate this, libertarian conservatism would. Even if the harm principle is respected to a certain degree, the implicit enforcement of monist values on other individuals reduces the pluralism of values and therefore is a restriction of liberty in society. This is why we should be wary about identifying anything or anybody who claims to be freedom-loving and advocating individual liberty with liberalism. This is not true until a truly free society is advocated too.