First off, many things in life are paradoxical which not necessarily invalidates them. For example, for humanity to live each of us living today have to die. Human life requiring our paradoxical death. Another example, for freedom to exist paradoxical rules must be deployed to protect a vile-maxim of individual freedoms from damaging our collective freedom. So, a paradoxical stance can clearly be a valid one and should not be discounted off the cuff.
I am not a politician, nor is my interpretation of a new operating-system for humanity to outlive a fly politically motivated, and I will therefore not comment on the suppositions of B. Shapiro. I suggest you ask him directly.
Second, we do not have free-markets anywhere in the world today, but instead, deploy merely various degrees of a pretense of freedom. For all our freedoms are oligarchically controlled by stale monisms of absolutism, quite the opposite of the freedom of freedom that makes freedom free. For real freedom is a relativity theory, to each his own. So, our current pretense of free-markets is quite the opposite of free, despite freedom being quite easily sloshed around in the catacombs of Congress, without anyone able to clearly define freedom, as I discovered in my visits to Congress.
Third, and treading the political knife-edge carefully, you simply cannot be a conservative and wholeheartedly believe in freedom. For the freedom of freedom is a relativity theory that obliterates downstream optimizations of the past with periodic upstream renewal of a new and better normalization of a foregone truth. Hence, the very stance of conservatism, holding on to an unwavering truth, proven wrong in the face of continual and expanding discovery of our universe, is in direct conflict with the rules of nature and evolution, in general, towards advancing human excellence.
Fourth, freedom (as covered in my second point) requires paradoxical rules, and roughly the same amount of rules, regardless of the marketplace construct of your choosing. For the simple reason that the participants and bad apples are bound to be of the same composition. Hence, a position to enable a free marketplace can constitute either rules managed by the marketplace itself and/or managed by the government. And sometimes, to enable freedom in a marketplace chockfull of bad behavior (from unbridled freedom) requires harsh and impactful paradoxical rules that put a severe smackdown on its current participants.
So, again, ask B. Shapiro which one of the four primary elements listed here cemented his current stance. I am sure he has a vested interest in informing his constituents about what may or may not reelect him.