For me, it really depends upon the type of influence and how that influence is initiated (i.e. by the child or not).
When my youngest DS went to school (the local C of E school selected for him by the local government) he went very quickly (within a week) from being someone who didn't believe, into a child that very much believed.
On his first day at school he was told off for not praying in assembly, which made him really upset (because he didn't want to pray because he didn't believe), but very quickly he was brainwashed by it all and was continually talking about god.
In this instance, since it was the school who seemed to be quite forceful with a religious perspective, I countered it with quite a lot of science based education at home. I discussed with him how he should always look for evidence and facts and not believe everything he is told just because it is written in a book/newspaper or on the internet). By the end of the first term at school, he had given up on his imaginary friend and now continues to an excellent inquisitive and questioning attitude.
With that said, if he decided that he wanted to find out more about a religion, then I would be very happy to help him. As long as it is his own choice.
He is now 6 years old and I have great fun being challenged by him on things like Father Christmas and the Tooth Fairy. We discuss how there are a number of different possibilities with Father Christmas, and how he might travel at Mach 6000 (6000 times the speed of sound), or how he might use wormholes to jump through time/space, but tell him that it is up to him to decide if he exists or not. I haven't told him the other scientifically possible theory for Father Christmas, which is that Father Christmas has franchised out the present delivery to an army of parents whilst he sits on his fat arse at home! He is sure that he doesn't exist, and plans to stay up all night to prove it (which I am all up for, knowing that he won't manage it, so it will keep the fun going another year). The funny (and impressive) thing is, he won't commit 100% to not believing in Father Christmas until he has this last piece of evidence, and is still willing to hedge his bets!
He keep saying that the tooth fairy doesn't exist, and I tell him that he needs to make a decision based upon the facts (on the day his first tooth falls out), and if he is right, then he will get double the money under his pillow.
Some might say that it is hypocritical to talk about Father Christmas, but not encourage him to pray at school, but there is a critical difference. Firstly, it is my choice as a parent as to what religion/mystique I enforce upon my own children (and not that of the state). Secondly, Father Christmas and the Tooth Fairy is all part of the process of learning that people lie for political gain. I tell them to behave otherwise Father Christmas won't bring them presents. Churches and the state tell society to behave otherwise they will go to hell. It is nice that they learn the truth about religion in a fun way.