No. To paraphrase the late Joseph Overton, former executive vice president of the Mackinac Center for Public Policy, to call a person a conservative because they support a free-market economy and property rights is like calling someone a vegetarian because they like green beans. The same is true of institutes that support free-markets over command and control economics. There are many varieties of conservatism; one of those varieties is people who are fiscally conservative and socially liberal. They are libertarians.
CRI's philosophical roots can be traced to Henry David Thoreau, Patrick Henry, Thomas Jefferson, Rose Wilder Lane, John Locke, James Madison, George Mason, Ayn Rand, and Adam Smith. Contemporary equivalents include Milton Friedman, Friedrich A. Hayek, Ludwig von Mises, Charles Murray, P.J. O'Rourke, Thomas Sowell, and Walter Williams.