I always liked the idea of having one policy in piety being a faith spender to provide an outlet if you (have to) form a religion with many faith generators in it. These can be the monastery, since every religion has monks and nuns of some sort, but with a different effect, holy warriors fit well as well (but then there'd need to be another war-based belief imho).
I'd like to see a free temple in the piety opener. The building itself comes later, but religious societies did have big temples early on after all

Add in a small culture or faith effect and you have a solid one. Also helps with one of the next policies giving gold to temples which you'd otherwise have to research first...
I do think there can be one or two effect linked to a religion, I'd particulary like "funded cities get your religion" added to the trade one above. With a "spend faith policy", this already gets crowded and kinda jack-all, but still interesting.
As for Honor, I like the idea of a bit of expansion thrown in, but the tree already gets very crowded. I like early direct bonuses and would like to see policy number 1 coming a few turns earlier. I was thinking of coupling Honor a bit with Exploration instead. First, is it possible to change the reward of clearing barbarian camps to the script given by ruins? They are more fun (even if more unstable and thus more imbalanced, but hey...). I'd like to try that

I'd then have the opener be: Free high XP Scout, Barb culture and combat bonus, and one policy be: Double bonus for Ruins, barb camps, meeting CS + Reveal Barb Camps + bonus that stays). The problem here is obviously that you'd nee to go for it to get the maximum effort and even then it might still be too late on small maps. So it needs something to be able to be picked later on (gold bonus for CS backwards compatible, less upkeep or something).
Honor should be the policy tree that lets you get a head start. There's not much to conquer yet so the abilities regarding puppets et all just come into play later. Up until then, it'd should get bonuses that propel you forward, like the free settler, no isolation malus, free garissons.
Liberty on the other hand should help you build all your cities up and link them together: Workers, Building Bonuses, faster border expansion, free trade unit, etc.
While Tradition is focused on your one city and rewards that city growing by per-population bonuses and Piety gives you general bonuses that you can later on shape when you know more about your surroundings (via faith and religion and gold (spending)).