//New Judge, is God mentioned in Civil Partnership or Register Service?//
Not as far as I know. Your point being what, exactly?
People who want to "legalise" their partnership have the option to marry in a religious establishment or do so in a Register Office or elsewhere licenced for weddings. Those who want their God to bless their union choose the former, those who don't choose the latter. Just what is it about a Civil Partnership that is not satisfied by a civil wedding? I used the word "justification" because I cannot see any reason for Civil Partnerships. They were introduced to address a problem and that problem has now been solved.
//Marriage has always been a religious, misogynistic type of ceremony...//
What on Earth do you mean, pixie? It doesn't have to be religious (see above) and why do you consider marriage to be misogynistic (i.e. the hatred of, contempt for or prejudice against women)?
//I wouldn't make a Civil Partnership the same at all, but make sure it was different....//
How (and why)? It is a ceremony to mark a union between two people. DO you want to make a circus of it?