Separating Church and State

Someone suggested this in print a couple of days ago, and I think it’s a great idea: separate the institution of “marriage” as a religious sacrament from “civil union” as a legal relationship.
It seems to me that the current debate mixes secular concerns with religious convictions. As a member of the intelligentsia in an old Jules Feiffer cartoon intoned following a scatalogical exchange: “Let us define your terms”.
I think the government has no business giving “marriage” licenses. “Marriage” is a religious sacrament. We don’t ask government to play a regulatory role in any other event associated with a religious observance, for example, baptisms or Bar/Bat Mitzvahs.
We DO – and quite properly so – expect government to regulate and adjudicate contractual obligations between people. The legal and tax ramifications of adults living together in a committed relationship are a legitimate government concern. The emotional and spiritual aspects are, frankly, none of government’s business.
Why not, then, separate the terms marriage and civil union, leaving one to the church and one to the state.
The government would continue to grant some form of recognition of committed unions, making people eligible for applicable rights and responsibilities within civil law.
Marriage would continue to have a religious meaning appropriate to the beliefs and traditions of the people involved. Furthermore, religious leaders would have the same authority they have now, to conduct marriage ceremonies for particular couples, or not, based on their own convictions.
No pun intended, but I think this entire rancorous “wedge” issue would disappear if these two concepts were de-coupled.
And you wouldn’t even need a constitutional amendment to do it.