How to get the Theology tech

If you still care about your production of other resources, the optimal strategy is probably to sacrifice your faith immediately before resetting the game as a whole, and only then. Sacrificing your faith at any other time (especially if you've sacrificed it before) will give you a large hit to your general production in exchange for a small boost to your total faith generation, which probably isn't worth it.

If you really only care about sacrificing as much faith as possible in the end, then it gets murkier, and as you said, the math is complex. The only thing I'm sure of is that you shouldn't sacrifice your faith if the production bonus from your faith is lower than your faith bonus due to sacrificing, unless you're about to reset the game as a whole. I would probably sacrifice once my faith production bonus is double my faith sacrifice bonus (but again, only if I'm willing to cut most of my other production to speed up faith generation).

Edit: At some point after this answer was written, the faith bonus was nerfed: it now begins to suffer diminishing returns at 750%, and is hard capped at 1000%. If you're able to store enough faith to quickly get your faith bonus over 750% after sacrificing faith, then it makes sense to begin sacrificing faith often. (The Apocrypha bonus has no such diminishing returns.)

When you have 25 Alicorns there will be an option in the Religion tab to Sacrifice your Alicorns.

Here is the code

dojo.declare("com.nuclearunicorn.game.ui.SacrificeAlicornsBtn", com.nuclearunicorn.game.ui.ButtonModern, {

    onClick: function(){
        this.animate();

        if (this.enabled && this.hasResources()){
            this.payPrice();
            this.sacrifice(1);
        }
    },

    sacrifice: function(amt){
        var amt = amt || 1;
        var alicornsCount = 25 * amt;

        this.game.msg(alicornsCount + " alicorns banished. You've got " + amt + " time crystals!");
        this.game.resPool.get("timeCrystal").value += amt;
    },

    updateVisible: function(){
        this.setVisible(this.game.resPool.get("alicorn").value >= 25);
    }
});