I think that both men where quite religious and Christian isn't a coincidence in this case. There is very much a set of values that neither reaction nor liberalism can regenerate out of the old Western tradition that they inherited since they lack the memetic technology to do so and the socioeconomic circumstances aren't favourable either.

I see this in many different kinds of values where there is a serious gap between say atheist Christian raised parents would like to transmit but can't to their children since they don't have good arguments that would make sense in their framework if the latter is taken seriously. Now as the one or two conservatives reading this probably realize people don't take frameworks seriously so inertia does transmit some of it in a pre-rational manner. I dread to think what my ehtics would be like if all of it was derived from some set of axiomisable first principles without the unique prejudices and eclectic mix of impressions and infections that I've collected over my life...

Note this probably generalizes to any exposure to ideologies. Once you reject a certain framework cached thoughts from that system of thought remain and influence your values, sometimes even constituting key parts of your value system. But this does not mean you have retained the correct tools needed to infect other people or even your future self with these values.

Humans are broken in this regard, the best we can hope for is setting up resilient traditions and reducing memetic mutation as much as possible and ... but those seems pretty antithetical to technological progress. So our society is very much like an artificial intelligence that can either chose to stagnate and be certain in keeping its current value set or self-improve in capability but risk accidental changing it. This isn't all that's going on of course, but I think it is a real trade off that modern man is incapable of considering properly.