Piety opener doubles your production towards shrines and temples. One way to capitalize on this bonus is to micromanage building shrines and temples to get them almost finished, e.g. put 39 out of 40 hammers (standard speed) into a shrine, then lock all your production tiles and get a lot of hammer overflow for the next item in your build queue.
What's more interesting is that once a city hits 40 hammers per turn, you can sell your shrine, build it on the same turn and not lose any hammers since you get 40 overflow. In fact, you GAIN hammers if your city production is over 40 hammers. Let's say your city is at 60 hammers per turn. You sell the shrine, build it at 120 hpt and get 80 overflow towards whatever you actually want to build vs 60 hammers you'd get normally with one turn of production. You also get 10 gold from selling the shrine, and you don't even lose any faith because the game processes production first. You can do this every other turn, so it's a pretty good boost to your production and gold.
What's more interesting is that once a city hits 40 hammers per turn, you can sell your shrine, build it on the same turn and not lose any hammers since you get 40 overflow. In fact, you GAIN hammers if your city production is over 40 hammers. Let's say your city is at 60 hammers per turn. You sell the shrine, build it at 120 hpt and get 80 overflow towards whatever you actually want to build vs 60 hammers you'd get normally with one turn of production. You also get 10 gold from selling the shrine, and you don't even lose any faith because the game processes production first. You can do this every other turn, so it's a pretty good boost to your production and gold.