Dark and inscrutable are the ways by which we come into the world. The instincts which give rise to this mysterious process of nature are not of our making. But out of physical causes, unknown to us, perhaps unknowable, arise moral duties, which, as we are able perfectly to comprehend, we are bound indispensably to perform. Parents may not be consenting to their moral relation; but consenting or not, they are bound to a long train of burthensome duties towards those with whom they have never made a convention of any sort. Children are not consenting to their relation, but their relation, without their actual consent, binds them to its duties; or rather it implies their consent because the presumed consent of every rational creature is in unison with the predisposed order of things. Men come in that manner into a community with the social state of their parents, endowed with all the benefits, loaded with all the duties of their situation. If the social ties and ligaments, spun out of those physical relations which are the elements of the commonwealth, in most cases begin, and always continue, independently of our will, so without any stipulation, on our part, are we bound by that relation called our country, which comprehends (as it has been well said) “all the charities of all.” Nor are we left without powerful instincts to make this duty as dear and grateful to us, as it is awful and coercive.And then the question of whether or not it's "consistent" with Hayek is posed. My answer, which I've largely copied from a comment on the post but expanded, is as follows:
The Burke passage deliberately runs together a couple of things that should have been kept distinct. First, as many have pointed out, he conflates a child’s duty to his parents with a citizen’s duty to her state, as though the state really were a kind of parent figure and the citizens permanent juveniles. And second, he mixes moral with legal obligation, as though the state could legitimately coerce any sort of good behavior.
Hayek, I think, would understand and appreciate the idea that there are many aspects of tradition, custom, even common law, that have evolved for reasons we don’t necessarily fully grasp, and that we should therefore be cautious about abandoning or overturning. But he would also say that we can’t stop there, because there are also many aspects of our cultural inheritance that are remnants of earlier superstition, ignorance, and bigotry. And he wouldn’t have made the sort of rhetorical confusions above, that Burke indulges too readily.