Should churches marry members of the public?

Recently I heard an interview on Radio New Zealand National in which lawyer Grant Ilingworth discussed some of the legal implications of the Marriage Equality bill currently before parliament.  His view is that, as churches marry members of the general public, they wouldn't be able to refuse to marry a couple on the grounds that they were of the same sex.  Institutions that offer services to the public are covered by the Bill of Rights (IIRC), which states that such institutions can't discriminate on the grounds of sexual orientation.

His view doesn't appear to be uncontested, but regardless, it led me to what I suspect is an important question.  Should churches be marrying members of the public (as opposed to only marrying people within our own church communities)?

The disquiet in the Christian community at the prospect of same-sex marriages seems to hinge on the idea that such marriages are unbiblical.  However, is it only same-sex marriages that fail this test?

An opinion piece in a recent edition of The Baptist included this sentence:

Ephesians 5:22-33 provides us with the Apostle Paul’s pattern for how this male/female marriage is to function as an outworking of a man and woman’s mutual confession of their sin and faith in Christ, which forms the glue to their convental commitment with one another in marriage.

When I got married I was conscious of making a covenantal commitment in the presence of God and my community.  However, many of my married non-Christian friends don't even believe that God exists.  They certainly haven't made a "confession of their sin and faith in Christ" at any point, nor were they calling on God to bear witness at the time of their marriage.  It seems to me that their marriages aren't any more Biblical than a same-sex marriage.

Hence my question: should the Church solemnise such marriages?  Especially if we are unwilling to solemnise other marriages on the grounds that they are unbiblical.

Such a policy would mean that all marriages conducted by churches would have to meet whatever conditions the Church (or church) thought necessary in order for the marriage to be genuinely Biblical.  It is highly unlikely that such a policy would prevent clergy from ever being asked to marry same-sex couples, but it would mean that they would be able to respond to such a request by discussing its Biblical merits.  Potentially even by asking the couple why they felt that it was appropriate for them, as Christians, to contract such a marriage.

Were we to refuse to marry any couples from outside of the Christian community, that would presumably also have the handy extra consequence of preventing us from falling foul of the sexual orientation discrimination provisions in the Bill of Rights as we would no longer be an institution offering a service to the public.