1. To what extent does manosphere ("red pill") teachings intersect with traditional religious doctrine?
Men chase after women thinking they will love them unconditionally much like their mothers did. Shattering this illusion, shatters many other illusions, for one the idea of comfort. You realise that everything you get in life, comes from the quality of life you lead. Your actions, your thoughts, it can be daunting to realise that this can collapse and you are fundamentally on your own. Paradoxically such a realisation will make you work harder and take on an attitude which is very positive in the manner of getting things done.
Want to get better with women ? Go out and approach.
Want to make money ? Work, learn a new skill and push hard.
Want an interesting life ? Go traveling, keep your wits with you.
So where does religion play into this ? when you realising that there is no absolute to be found in the material, you will look further a field for such deeper sensations. Much like after a work out or engaging in something constructive, you get this positive creative buzz. Tapping into a path of religion/spiritualism, meditating, leads to a wholeness which you just fail to get with short term gratification.
2. Are we likely to see a revival of traditional religion, as a backlash against feminist excesses?
We are already seeing this, I believe the conflict in the Middle East, is a direct result of the "clash of civilisations" that Huntington mentioned after the Cold War. You have a democratic order which wishes everyone to become a easily managed politically correct consumer. Then you have the polar opposite of that, with Islam probably equally irrational but on the stance of preserving a non material, patriarchal order. This is the ultimate clash if you ever could see one, far shadowing the crusades. Make no mistake about it, the seemingly atheist West, has all the same religious sentiments as the so called dogmatic types, which it seeks to undermine.
Even in the U.K, around Inner London, well most urban areas now, you see this growing counter culture movement growing. Not in the Hipster/Vice tv fashion, but with African christians, muslims all rejecting this culture on the grounds of satanic conspiracy, but fundamentally they are aware that only a rich country can be so irresponsible like this. People are turning to Islam for this grounding certainty, especially those from inner cities, who come from different non Asian backgrounds. Albeit not in large numbers, it is certainly growing.
3. Will traditional institutions continue to function, as they did in the remote past, as preservers of traditional civilization in the face of barbarian onslaughts?
First I believe its important to not conjure up images of tradition being akin to belonging in the path. Traditions were trial and tested for thousands of years in order to become so rigidly enforced by successful civilisations. They are merely practical organic functions, I state that they are organic, because although they required force and government legislation in some cases. They were no where near as enforced as incentivised as the cultural revolution of the 1960s, and all of their "liberalisation". We have a lot of incentives and unnatural pressure to create the state of affairs which we have right now in the Anglosphere.
I geniunely don't see this holding any weight if we were to have a significant economic depression. People would revert quickly back to traditional gender roles. Those who are too far gone, simply won't survive, same thing will happen if we went back to a free market.
Either way i don't see the Othordox church in Russia and EE backing down. They have been overtly attacked for a long time, and although factions of them are liberal. There are still plenty who are intellectually aware of whats going on.