It is erroneous to call such people "Bible-believing."
What is the difference between liberals, progressives, socialists, communists and liars? (As for me, I don't see any.)
Try visiting a "happy-clappy" church. They will all be holding their NIV Bibles while being entertained for an hour or so. They will be anti-abortion and will mostly vote Republican, but they won't tolerate traditional worship.