But that's what I don't understand. Either God 'A' who is believed by Religion 'X' exists or doesn't exist. If 'A' exists, then even if 'X' didn't believe in 'A', 'A' would still exist. (At least assuming that 'X' is a subset of all religions that I know) If 'A' doesn't exist then 'X' believing in it doesn't make 'A' exist anymore.

I can't think of any religion where pure belief of people cause deities pop into existence. Unless of course you are calling the fact that people talk about the deity as popping them into existence. In that case, you can say that JK Rowling caused Voldemort to pop into existence (how evil of her).