To me it is clear that marriage in the context of any discussion of law should mean a union of two people as it pertains to legal issues. I don't understand why people need to drag in the religious baggage.

Exactly, and since marriage comes with religious baggage attached and
There are plenty of words in the english language that mean different things based on context and personal viewpoint.

then there should be no problem finding a new one, right?

I think "civil-union" has an excelent ring to it, don't you?
_________________________
___________________
- Marcus -