No, because that situation is different. The definition of a county clerk's job includes issuing licenses; I would expect it's a fairly explicit requirement, and taking the position means one agrees to those requirements. OTOH, a doctor who objects to abortion would never take a position where doing abortions was a job requirement.
The State coming along after the fact and adding such a requirement is IMO unlawful and unconstitutional.
> And soldiers must obey what they believe as unlawful orders
Soldiers are in a difficult position in that regard because their explicit job requirement is "Do what you are ordered to do, regardless" and they agree to that when they sign up. If they are later given an unconscionable order, they are in a tough spot because refusing to follow orders carries a large penalty, but if they make a stand, they are accepting that penalty.
So, if you're in a government position that asks you to perform against your religious convictions/creed, your options are to act against your conscience or find another job? Freedom of religion does not end when we step outside a church as many would like us to believe. Liberty is not license; it is the freedom to agree or disagree. There needs to be accommodation and respect for the religious convictions of individuals both in and out of government. It is presently lacking.