Possible solution to US marriage equality issue

[Knee]

The problem as I understand it:
A) Not allowing non-heterosexual couples to marry is discriminatory and creates a situation where not all US citizens have access to the same rights/privileges.
B) Some religious folks say marriage is a religious institution and non-heterosexuality is against their religion, so forcing them to accept non-hetero marriage infringes upon their religious rights (I think this is the basic argument.)

(I understand that there are more arguments against, but I think the only one I've heard that doesn't sound like basic homophobia to me is the one mentioned above.)

My solution:
1) Make marriage a purely social and/or religious concern. The government no longer cares whether you are married. You are still a single person in the eyes of the government. Churches and other organizations are allowed to make their own determinations regarding their ceremonies and who can be joined in matrimony.
2) Take all of the rights/privileges/what-have-you that used to be associated with being married away from marriage.
3) Give the rights/privileges/what-have-you to civil unions.
4) Allow any two consenting adults to get a civil union at their local courthouse, or wherever.

Results:
I. Everyone gets the same rights provided they are willing to go get a civil union.
II. The 'that's against my religion' argument no longer holds water because the government isn't forcing anyone to accept gay marriage.
III. Separation of church and state achieved in the process! Success!
IV. The government still has a way to encourage people to pair up. Our government likes happy little stable family units for all kinds of reasons.
V. If you can find someone willing to perform your marriage ceremony, you can still get married, no matter who the two of you are, because it no longer has to be legal. It's just a guy at a church going "why yes, we accept and love our non-hetero brethren and will happily perform a marriage for you, even though it is now worthless to anyone but you and your family and friends.")

Basically, people want to keep their precious marriage institution all pure and godly? Fine, let them have it. It was originally a religious thing anyway, wasn't it?

What do you guys think?