I was taken to church every week as a child. We were only allowed to take religious picture books. It was mostly incredibly boring, and oh how I envied those children who were allowed to bring action figures. I am now an aetheist with a great capacity for daydreaming whilst looking attentive.
I think a nintendo is not appropriate, but cannot for the life of me understand why books and quiet toys are held to be not allowed for a child who is not a churchgoer, and who probably does not have any religious beliefs. If it was a situation where his parents could talk to him and explain what is going on, then fair enough, but as she will be being quiet too, that won't really work.
I have a very active child who has major problems keeping still (and dd who is fairly good at this). I carry a bag with cards, books, and yes two DSs. I pull these things out when I can see ds is getting very restless in situations where he needs to be quiet and still(ish). I usually get comments about being well prepared, not bitching about what a terrible parent I am that I can't force my child to shut up.
We took ds once to a wedding. He spent the majority of the time running around the churchyard. I don't think that upset anyone. When we went to a family funeral, again after a while dh took the children out. Discretely. I really can't see this as a big deal.
My children spend lots of time outside, play great imaginative games, enjoy a good book and can sustain a pretty decent conversation. At other times they like to play on their DSs and other electronic kit. So do I.