The sequence of events are in conflict. Genesis says that the earth was formed before the sun and the stars, while Big Bang cosmology says that the earth formed after. And, of course, the Genesis claim of the universe forming as we currently know it in only six days is totally incompatible with the Big Bang Theory, which suggests 15 billion years.
Now, I know that many Christians claim that if you "interpret" Genesis the right way, then it will all fit. That's fine with me and only proves my previous point. Christians are so deeply invested in the Bible that they must believe it's stories are true despite any apparently contradictory evidence, but they are also modern, rational people who cannot afford to dismiss mainstream science. So they force a compromise that explains that the Bible means something totally different from what it is apparently saying. I understand this tactic well because I used it all the time, myself, when I was religious -- I had to in order to keep my sanity. (To be sure, though, not all Christians rewrite the Bible when it encounters a direct challenge from science. Creationists, for example, do seem to be comfortable dismissing mainstream science when necessary.)
This is why I have no doubt that most Christians will have little trouble accommodating a multiverse. Personally, though, I see serious conflicts between a multiverse theory and any form of structured religious belief. After all, if there is a universe for every possible outcome of a quantum event, then there would have to be countless universes where people who are Christian in this universe are atheist, or buddhist, or muslim, or something else. Also, are there universes where Jesus was never born? Wouldn't there have to be? I don't see how it can possibly fit, but I'm fairly confident that there will be plenty of people telling me that there is no conflict at all.
What happened to the fundament?