This is a question asked at:
To which there is a short and very simple answer:
The 'neo-' in neoreaction signifies 'not-'.
If there ever was any serious doubt; every passing month shows more and more clearly that the neoreactionary, secular-right, alt-right, dark enlightenment movement are just a type of Leftism.
You can actually track the corruption of neoreaction, happening before your very eyes; in the going-down-the-tubes attitudes, style, focus and behaviour of individual bloggers.
(If it looks like Leftism, talks like Leftism, and in general behaves like Leftism - that it is Leftism - not least because the rare Western non-Leftists stand-out from modernity like a beacon, or a sore-thumb.)
Neoreactionaries dislike many aspects of mainstream Leftism, but not so much as they dislike religion.
That the only real-life reactionary societies have been and are religious - and if reactionaries were serious about being reactionary they would simply choose their religion.
Instead they prefer the cut-and-thrust, snark-and-sarcasm of (characteristically Leftist) speculation on how, somehow, it might be possible to construct a sustainable non-religious reactionary society of a kind that never was seen (but which includes all they stuff they like best, and not the stuff they hate: no need for hard choices here!).
But why are neoreactionaries they so hostile to religion?
There are many possible reasons for being personally non-religious, as I know from recent personal experience (especially a reluctance to abandon your preferred freedoms derived from the Leftist sexual revolution); but the answer (if you cannot yet be religious) is to become a religious seeker.
It is hard to rationalise or even excuse anti-religiousness in anyone who wants their self-defined 'reaction' to be serious, or to be taken-seriously.
However, whichever anti-religious reason applies in each particular instance, the conclusion remains the same: neoreactionaries are more serious about their anti-religion than about their pro-reaction - hence the 'neo-'.
See also: http://charltonteaching.blogspot.co.uk/2013/10/neoreactionaries-versus-religious.html
But what about the cadre of supposedly-religious neoreactionaries? What indeed... What do they hope to get from this unequal alliance? Could be they are simply mistaken in their assumption of a possible synergy between tough-minded- this-worldly hedonism on the one hand; and religion on the other. Or it could be they are led astray by the daily excitements and distractions, the status fun and games, the guilty pleasures of swearing and salaciousness - and the opportunities and inducements to hatred and hard-line-ism 'in a good cause'?