I share with you the following from The Alliance Defending Freedom for Faith and Justice:

"There is a common misconception that pastors who sign marriage licenses have become "agents" of the state who could be forced to perform same-sex weddings. That is false. Just because an individual has permission to act does not mean that the state can force that person to act. For example, motorists obtain state permission to drive on public roads, but the state cannot require them to drive. Similarly, pastors are authorized to sign a marriage license, but they cannot be required to perform marriages.
Pastors are not acting on the state's behalf. For now, they still enjoy the same religious freedom they have exercised for decades: the right to decide who they will – and will not – marry."
"There are a host of practical concerns that should cause pastors to think very critically and prayerfully before deciding to stop signing state marriage licenses. By refusing to sign marriage licenses, are pastors participating in the further deterioration of an institution that society – and particularly children – desperately needs? Is such a step practically necessary when there are currently no attempts to force pastors to perform weddings that violate their faith?"
"Consider also the legal ramifications for a couple that is religiously married, but not civilly married. Civil marriage affects property right, assumptions of paternity, probate and inheritance rights, family visitation rights, and numerous other legal issues. How will these legal matters be addressed? And if pastors do encourage couples to obtain a separate civil marriage, why is it appropriate for congregants to do something (sign a marriage license) that pastors will not?"
The following is NOT from the above-quoted Alliance Defending Freedom, but are my thoughts:
Occasionally our pastors have been asked to perform "religious" weddings that do not notify the state, that is, there is no civil license obtained, signed, or recorded with the state. Pastors may not agree to perform such weddings. In addition to the legal problems this raises as noted above, there is this: Oftentimes these are requested in order to retain certain financial benefits that would disappear should the state or other entities find out a person has remarried. This can amount to defrauding those who are paying certain survivor pension or insurance benefits and is certain to invite inquiry by the IRS. Being complicit in such a matter could lead to legal penalties for the pastor and for his congregation. If loss of financial benefit is the reason, I'm sure the AARP or some other group would be pleased to lobby the government to change the laws!