I was raised slightly Episcopalian, my family moved around a lot and didn't go to church much, so I am reluctant to claim it as my religion. Actually, I am currently disenchanted with organized religion, and am sort of marching to the beat of my own drummer.
Oops, I forgot to add how it affects me and Tarot. Sorry bout that . . . I think that it has made me a very open minded person not to really be involved in any religion. I went on a kick a while back that I did a lot of research on different religions and realized that most religions have both good points and bad points. As with anything else, I think religion is what you make of it.
Regarding Tarot, I think that because I lack any real religious beliefs my involvement with the cards may actually help to bridge that gap. Not that I worship the cards or anything like that, but I find that when I am troubled sitting down with my deck and doing a reading seems to soothe me. So, I'd find that ritual possibly similar to a religious service, for me. I'm not sure if I'm explaining it right, but when reading I seem to go into an almost meditative state. So I think perhaps it is similar to what others feel when in prayer. Not that I don't ever pray, but not as a ritual. If that makes sense . . .