[Ostlandr]

Wouldn't it be rather ludicrous and pointless to make an Atheist or Satanist swear on the Bible?

And wouldn't a devout Muslim be more likely to give true testimony if they swore on the Q'ran?

No matter what oaths are sworn, there are always oath-breakers, perjurers and liars.

Much as I hate to agree with the Left, what's wrong with "Upon my honor, and under penalty of perjury, I so do swear."

[Prime Choice]

And wouldn't a devout Muslim be more likely to give true testimony if they swore on the Q'ran?

Nope. Islam provides for lying to (or about) non-Muslims.

[Michael Barnes]

You bring up an interesting point. What do today's courts do with atheists?

[Cboldt]

Much as I hate to agree with the Left, what's wrong with "Upon my honor, and under penalty of perjury, I so do swear."

It's not so much "agreement with the left" as it is seeking supremacy of law over religion. The law fancies itself to be the ultimate force on earth.