Yes, Fundamentalists will scream bloody murder that is a given. However, there is a big difference in peoples minds between fiction and reality. It's easy to suspend disbelief, it's something else entirely to accept it as truth.
Go up to almost anyone and strike up a conversation about the possibility of Parallel Worlds and how it is seriously being considered and they'd think you were nuts. They'd likely rank you right up there with folks who claim to be abducted by aliens on a nightly basis.
Hell! Just to prove my point I decided to do a little Google to see how many Americans actually believe in the Virgin Birth of Jesus Christ.
Taken from Newsweek:
"Sixty-seven percent say they believe that the entire story of Christmas—the Virgin Birth, the angelic proclamation to the shepherds, the Star of Bethlehem and the Wise Men from the East—is historically accurate. Twenty-four percent of Americans believe the story of Christmas is a theological invention written to affirm faith in Jesus Christ, the poll shows. In general, say 55 percent of those polled, every word of the Bible is literally accurate. Thirty-eight percent do not believe that about the Bible.
In the NEWSWEEK poll, 93 percent of Americans say they believe Jesus Christ actually lived and 82 percent believe Jesus Christ was God or the Son of God. Fifty-two percent of all those polled believe, as the Bible proclaims, that Jesus will return to earth someday; 21 percent do not believe it. Fifteen percent believe Jesus will return in their lifetime; 47 percent do not, the poll shows.
When asked if there would be more or less kindness in the world today if there had never been a Jesus, 61 percent of all those polled say there would be less kindness. Forty-seven percent say there would be more war if there had never been a Jesus (16 percent say less, 26 percent say the same); 63 percent say there would be less charity; 58 percent say there would be less tolerance; 59 percent say there would be less personal happiness and 38 percent say there would be less religious divisions (21 percent say more and 26 percent say the same)."
http://www.msnbc.msn.com/id/6650997/site/newsweek/Most of that is MORE THAN HALF of the United States of America. Many Worlds Theory would basically say to them - to any religion - that their chosen one, indeed their entire religion, does not exist in other worlds. You would basically be telling a Christian that in some world out there Jesus never bothered to show up. You'd be telling Jews that in a world out there Moses remained a slave, or was never even born.
...and you have to remember that you'd be telling this to people who literally believe the Bible is a literal interpretation of history. Those people represent more than half of the United States.
Of course, I think the culture conflict would be the least of it as it could dramatically alter how we view ourselves as people and the way we see the world.