I've been trying out that change to the Piety opener of giving +1 culture, +1 faith and double production for building shrines lately. It seems pretty balanced. In some games I select it as a first policy, but typically only games where I'm a very religious civ and I want a dominant religion. In games where religion is less of a priority, then I select the Liberty, Tradition, or Honor openers first.
Right now I'm playing with the 4 openers like this:
Honor: Culture from barbarian kills, +25% combat strength vs. barbarians
Piety: +1 faith, +1 culture (in capital), Double Production for shrines
Liberty: +1 production, +1 culture per city
Tradition: +3 culture in the capital
Tradition is the way to go if you aren't planning on expanding that fast. Maybe you are a tall civ. Maybe there just aren't any good places to expand to close by. Maybe you have very close, but pretty peaceful neighbors.
Liberty is the way to go for rapid expansion.
Honor is the way to go if you plan on going to war soon. I also go with Honor if there's lot of bad land around me where barbarians will be spawning. I believe that I increased the culture from barbarian kills slightly too and got rid of the revealing barb camps messages. That's more of a gameplay style preference than a balance change. I found the messages showing barb camps to be annoying and a bit gamey. I like it when finding a camp is a surprise. Just a preference.
I now go with the Piety opener if I want to get a pantheon up and going. Typically, it's only the first policy I pick if I'm a civilization who needs a dominant religion, such as Spain. Other policies give better non-faith benefits.