I like the initiative, it is sorely needed. I would try to avoid making the policy trees to similar to make them a specialisation for the civilisation. The one thing that all of them need is a bit of culture for policy aquisition and happiness for early population growth or new cities.
With piety I would do like this:
Opener: build shrines in half the time, shrines provides +1 faith and culture
Almost guarantees a pantheon, what you need early. If you play as maya you can stop at this point.
Organized religion: build temples in half the time, temples provides +1 faith and culture, temples increase the gold output of a city by 10%
Makes temples decent by gathering all the bonii in the same policy. Good if you make a temple/shrine religon. If you have a special temple building you can stop at this point.
Righteousness: the cost of purchasing religous units and buildings with is decreased by 20 %
No change except the name which did not fit.
Reformation: (requires Organized Religion)
No change except the required policies. Having to take policies just to get a new one is not fun so I put it after the genrally useful policies.
The Holy Land: Holy sites provides a combat bonus of 20% to units of their civilisation within adjacent tiles. Holy sites give + 3 gold +3 culture.
The same as temples, collect the bonuses in one policy. Holy sites may actually be worthwhile with this policy. (use the moai code for the first effect)
Religous Tolerance: Cities benefits from pantheon beliefs as before. 4 Global happiness.
Piety needs some happiness and religous tolerance is generally not useful, though occasionally brilliant (say if someone took desert faith from you). Since it is specialised it is better to remove it from the main chain to reformation.
Finisher: Free Great prophet, does not count towards your great prophet counter.
The problem with "free" great prophets is that the cost increase so rapidly that a free great prophet is a small bonus. If you can not code that, give dicount on future prophets of 25%.
With honour I would give the player a free warrior in the opener to go barb hunting. You do not need more bonii on military tradition, it is already really good. I like the new warrior code. I think you should de-emphasize military buildings/garrisons and instead give bonuses to unit maintenance and to puppet cities. How about giving professional army -15% unit maintenance instead of gold from buildings and the finisher halving the increase in science costs from puppets cities/halving unhappiness from population in puppet cities.
As has been said about liberty, the opener is really weak. Add 1 gold per city. I liked the 5% prod bonus for republic as production is the main reason I go for liberty it and the 5% is good all game. If you think it is weak, up it to 10%. The main inhibitor to growth with liberty is happiness not food. However, adding happiness to markets is problematic as it comes quite late is on a specialised building and overlaps with capitalism in freedom.
I like the limiting of free monuments and aqueducts to three cities. I would also remove the city attack effect from oligarchy and put the free aqueducts there. Without the bonus to city attack it will be easier to attack a tradition player before he gets too large tech advantage. Further, it mixes up the order for social policies in tradition, since getting an early aqueduct is a big advantage whereas the old oligarchy would almost always be picked last.
Another strange quirk is that tradition is good for small empires and liberty for large ones. Before the industrial era, republics were city states with a small territory and all larger political units were monarchies/theocracies. The major exception was Rome and the minor the Dutch republic which both gravitated towards monarchy as they grew larger but kept important points of republican ideology.