Once we recognise the problem the solution should be simple. First, marriage is two different things simutaneously. It is a religeous sacrament AND a legal contract. Note that it can be either one or both but usually is both.
Marriage was not a legal contract until circa 1756 when Britain passed a law to ensure that a wife got half of the union's assets when divorced. As a religeous sacrament it goes back thousands of years.
The solution to the "marriage" problem is simple. Just remove all references to "marriage", "married", and their synonyms from all laws, regulations, and other documets produced by all levels of government and replace them with something like "DP", defined by law to mean Domestic Partnership. (more in reply to this)