I use it a LOT more with an SPI civ than non-SPI, for the science benefit, biut for the most part, I stay in OR and Theo.
When I am conquering, I like OR to get those key building up fast in new cities. I also like OR early in the game as long as having a religion wont make me a target.
When I am building for war, I love Theo, its especially nice when drafting, since you get 1/2? the XP for a unit. Theo + barracks means my drafted units gets at least Combat I or Drill I.
I will use FR later in the game for Space races, the extra science is nice to go through those techs that are so expensive.
One of the reasons I like the AP is that you get the hammers no matter what religion or civic you are in. I generally try to capture or build the AP myself, jsut because of those hammers.