Isn't it a fact that our country was founded on Judeo-Christian principles? And so the Bible is the book that exemplifies those values? Even though we're not a theocracy, we tolerate other faiths or no faith at all, while still having Judeo-Christian values.
Whereas the Koran is incompatible with American values. So it's troubling to see someone swear on a book of a religion that is incompatible with America.
If a communist somehow were elected to Congress, would we be happy to see him or her swear an oath on the Communist Manifesto?
No. She'll be happy to swear on the Bible, just so long as she gets the power.
We already have many communist in congress and state department. They don't mind swearing on the Bible since they don't believe in any god whatsoever.