Soft Libertarians. Some of the most influential bloggers on the right, like Tyler Cowen, Alex Tabarrok and Megan McArdle, start from broadly libertarian premises but do not apply them in a doctrinaire way.
Many of these market-oriented writers emphasize that being pro-market is not the same as being pro-business. Luigi Zingales of the University of Chicago published an influential book, “A Capitalism for the People,” that took aim at crony capitalism. Tim Carney of The Washington Examiner does muckraking reporting on corporate-federal collusion. Rising star Derek Khanna wrote a heralded paper on intellectual property rights for the House Republican Study Committee that was withdrawn by higher-ups in the party, presumably because it differed from the usual lobbyist-driven position.
There are a number of unpredictable libertarian-leaning writers, including Conor Friedersdorf of The Atlantic on civil liberties issues, and Eugene Volokh on legal and free speech concerns.