Marriage is much more than a religious act. If it were only that, it would have as much meaning outside of ceremonial context as a Bar Mitzvah or a Confirmation does outside of the faith communities they originate in. If you tell someone you're married, it is relevant in secular society in a way that your admission to Level 5 in the cult of Scientology is not.
Google "legal marriage rights." The lgbt equality movement has done a great job underscoring just how many legal rights are conferred upon married couples in America. Marriage is a secular institution (but also a religious institution). Don't forget marriages can be done by Navy Captains or Justices of the Peace.
Non-believers have just as much of a right to the civil liberties our government developed around the institution of marriage, despite the fact that our modern concept of marriage has developed from a religious background.
It's a toughie. My fiancé is Christian, and because the Bible says people of different faiths should not be married under God, we're having trouble finding somewhere that will perform the ceremony.
I don't know about the US, but in the UK we can legally get married without the religious ceremony, however many atheists/agnostics choose to use a church simply for the tradition of it.
Maybe another argument for the separation of church and state?
As the preacher if his wife was a virgin on their marriage day. Unless he lies and says yes, you could ask him why he didn't stone her to death on her fathers door step... Just saying...
As a guy, I have a hard time with the thought that the person I want to be with in my 20s is the same person I will want to be with when I am 70. Maybe the marriage license should be more like a drivers license. Renew every four years or you lose it...
Completely secular ceremonies are easily possible in the US. Either at city hall or through a secular celebrant. Where much of Europe is far superior is that a civil ceremony is usually required in addition to an optional church wedding. Thank Napoleon for that. It makes it clear that it's the civil part that really counts.
Much of western Europe has a clear church/state separation about marriage. The US doesn't. It has a silly system where you get a marriage license at city hall and then anyone who is registered to perform marriages can sign it. That has the unfortunate effect that priests can perform a legally valid wedding and led many people to believe that you have to get married in a church.