The thing about the bibles in courts is true-ish. It used to be that anybody who believed in God could testify in court (and would be allowed to swear on their holy book, but they only had bibles in the courts so most people, christian or not, swore on that).
Atheists were banned from giving testimony as it was thought that since they don't fear divine retribution they couldn't be trusted to tell the truth.
The US has come a long way since these days of bigotry. They got rid of slavery too and gave women the right to vote
Whenever somebody brings up the "The USA was founded on Christian principles" line, I'm of course tempted to correct them by quoting all the founding fathers who spoke against Christianity (there are many such quotes). But then it occurs to me that this is a pointless exercise, for even if the country was formed on christian principles, that doesn't mean it should retain them or that they are in any way good for the country. Which is why I mention the country also being based on male chauvenism and slavery, two principles the country thankfully abandoned.
Oh and the old Christian society had some other strange legal ideas. So to Christians who judge Sharia law for being barbaric, I have to point out some things Christian theocracy came up with in its time in the spotlight. Both are called
judicium Dei (God's judgment):
-- Trial by ordeal, where witches and other's suspected of demon infestation were drowned to see if they died or not. If they lived they were possessed or a witch. If they died they were not and were sent to God, so it was ok to have killed them. Literaly a no win situation.
-- Trial by combat, where two people having a dispute would fight to the death and whoever won was right because God favored them in the fight. These people could hire champions to fight in their place and these champions are basically the first trial lawyers. A descendant of this, the honorable duel, remained legal until far more recent than you may think.