That's a false assertion. I don't care what people do in their personal lives but the issue of marriage and the strength of it is a societal issue. We've seen quite clearly how society is trending these days with marriage breaks down and what has occurred since marriage has decreased in the seriousness it was once held. Perhaps the 'religious right' are actually concerned about upholding something that is good for families (that children know and are brought up by their biological mother and father), good for society, and aren't keen to see something put forward that is likely to further diminish the status of marriage and result in kids being brought up without knowing their Mum or Dad. At least traditional marriage doesn't design this as an outcome right from the start.
I think it is more empowerment than a decline in seriousness. It wasn't that long ago when women were shunned for leaving their husbands. No matter how much of a boozer, wife basher, child basher or womaniser he may have been. The societal strength was that a woman had no way out of domestic violence for "what god has joined together, let no man separate". There was no support for women or children to escape from domestic violence or even just pure unhappiness in marriage.
I can only imagine what many women thought, sitting in church being lectured on the sanctity of marriage.