My wife wanted to marry me in a church, as she had (and still has) some faith. No church we spoke to would do it (understable), and one preist suggested my wife look around a bit further....for a more suitable husband.
I also testified at a murder trial once, and was handed a bible and asked to swear an oath. I didn't want to make a scene about my principles in a freakin' murder trial, and I didn't want to do anything that would weaken the prosecutions case...so I just did as I was told. I regret that a lot. I'm not quite sure it was perjury....but I felt like it was.
At the time of the promulgation of the United States constitution, there were quite a few Protestant sects which objected to taking oaths, many and perhaps most of which objected to taking an oath or making an affirmation on the bible. Therefore, the text of the Constitution states that the President: Before he enter on the Execution of his Office, he shall take the following Oath or Affirmation: "I do solemnly swear (or affirm) that I will . . ."
The language appears elsewhere in the document. If one were to refuse to swear, or to swear upon the bible, it likely wouldn't raise eyebrows in a U.S. court, except, perhaps, in very peculiar circumstances. I have testified more than once in criminal actions (although never in a murder trial), and have refused to swear upon a bible. It has simply meant that i was asked to affirm that i would tell the truth, the whole truth and nothing but the truth. This seems not to have prejudiced the cases, as in those examples, i was testitfying for the prosecution, which either won the case, or settled on their own terms. On one occasion, before a grand jury, i refused to so swear, and a couple of the 25 individuals assembled murmured, and the prosecution did not get a true bill (i.e., no charges were brought by the grand jury). However, in that case, i was asked if a set of statements by a police officer were true, and i denied them, because, frankly, the police officer had lied, and had attempted to put words into my mouth. The Prosecutor was enraged--i pointed out to him that he hadn't done his homework, because no one had contacted me to know what my testimony would be to compare it to the statement of the police officer. At all events, i believe in that case that my refusal to swear upon a bible was not a cause to invalidate my testimony.
I don't know what people's attitudes in Australia would be, but in the United States, i don't think such a refusal would excite any unfavorable comment or reaction.