- Does it serve a secular purpose? Yes. Many religious people are more likely to tell the truth after swearing on the Bible.
- Does it have a primary effect of advancing a particular religious belief? No. Requiring it, or treating different religious oaths differently would. But as long as you are neutral, it doesn't.
- Does it involve "excessive entanglement" of government and religion? No.
Furthermore tradition has a strong influence. Given that it has been accepted for centuries as part of our legal system, without very specific good cause, it won't change any time soon.
Cheers,
Ben