The big thing that I didn't realize until the credits started rolling was that it was based off of a true story. Given the content of the movie, that's really upsetting. Basically, Philomena deals with the phenomenon of forced adoptions in Ireland, and how nuns would go out of their way to make sure that adopted children were never reunited with their parents. The nuns were definitely the "bad guys" in this story, so I can think of a number of Catholics who would be upset by this film (my grandmother wasn't one of the, but I can see my sister having a fit over this), but it's not like the movie made up anything, since the nuns really did do this in real life. The movie makes sure to point out that they were bad examples of Catholics, though, and make Philomena out to be a good example. Sixsmith, meanwhile, was an agnostic, and overall the movie doesn't really take sides when it comes to religion, choosing to represent both worldviews sympatheticalkly. Politics are also lightly evoked, briefly, and the movie also does a good job of not taking sides in this arena as well.
One of the major characters was gay, and he was in real life. No big deal is made out of it, but it does affect the plot very slightly, so it's not as though it's completely ignored. He is depicted positively. I did my research, and the name of his lover was apparently changed, I'm guessing to keep his privacy. Overall, the movie is actually fairly close to real life.
So anyway, I'd recommend Philomena if you're in the mood for a decent true story, especially if you want something with a BBC atmosphere to it, since it definitely shows that this has a British director.