Sure, but when it comes to government it would no longer be an issue. My main goal here is to get government out of the middle of what "those people" try to conflate as being a religious issue.
As I said before, the religious angle is a rationalization. The real issue is homophobia. Taking away the word "marriage" to a purely religious relationship still leaves all the actual rights associated with marriage on the civil contract. And homophobes don't want gays to have those rights.
They already know that their religious arguments don't mean anything in court - so they aren't using religious arguments in court. They have arguments about child rearing and families instead. And those still hold if you change the word. Thus, no gain in changing the word.