Any unity capacious enough to contain both Hayekian liberalism and its opposite is too vague to be useful; any unity so narrowly tailored as to include only unchallenged points of general agreement is platitudinous. For example: Ocasio-Cortez advocates the so-called Green New Deal, and I oppose nearly every point of it — what chance for unity? We surely both agree that we would prefer clean air and clean water to pollution, a healthy environment to a less-healthy one, etc. — an inane unity that is of no practical use.
But calls for unity are not actually oriented toward the practical. They are spiritual mandates.
Presidential calls for unity express the increasingly sacral and quasi-monarchical character of the American presidency and the person of the president himself, who is treated as a kind of holy person, the body politic incarnate. The train of thought is there in the underlying etymologies: unity, community, communion. The American political superstition sets the Confucian model on its head, holding that if there is order in the nation then there will be order in the community and in the family, that our hearts will be made right in national democratic communion. Applied to American politics at large, that mysticalizing tendency is superstition; applied to the president in particular, it is idolatry.