I will argue that they should. Why? Two reasons. First, 'marriage' as a term is becoming meaningless and will only become even less so in the future. Second, if you don't perform 'marriages' at all, you cannot be sued for not performing same sex marriages.
Have you heard of the expression 'the sacred covenant of marriage?' Rather than marriages, churches should perform ceremonies of 'sacred covenants' (or a similar term). To officially be 'married', you would still have to go through the civil process.
And what, exactly would be a 'sacred covenant?' It would be a legal contract, signed by and binding on the two parties involved, and formalized by a ceremony. The contract would define the obligations of both parties involved as well as the conditions necessary to dissolve the contract. Denominations could design one or more 'standard' sacred covenant contracts, but it could also be individualized as well. The contract could specify how to adjudicate when there is conflict (e.g. church court, church appointed arbitrator, etc.).
And the benefits? In addition to the aforementioned two, sacred covenant contracts could be much stronger than current 'marriage' law. We have all been complaining for years about how the institution of marriage has been weakening. This is an opportunity to strengthen the whole business of 'for this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh', but on terms where it will be much harder for the government to interfere with. These will simply be private contracts between two individuals.
Homosexual activists and others on the Left would naturally scream about 're-defining' marriage. The irony would be delicious. Of course it might be best for some large organization (the SBC?) to copyright a term to use for these sacred covenant contracts, and only give permission for its use to churches that commit to using it solely for contracts between one man and one woman.
Thoughts? Although the SSM activists would have a fit, this would in no way infringe on their newly created right to get 'married'.