That's completely separate from the issue of freedom of religion though and an almost incomparable scenario because there are tons of institutions that can marry. It's not like people can just get the shall carry permit from anyone else. The analogy isn't bad but there's more to it than you seem to think
Edit: I misread OPs terribly worded post ignore this
English
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He didn't ask about someone denying them the marriage ceremony; he asked about refusing to grant a marriage license based on personal beliefs. The government grants marriage licenses, as far as I know they are the only ones who can grant a legally binding marriage license.
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Read the edit. OP worded his post horribly
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It's cool man, still love you.
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The issue isn't that they want to get married in a church. Sure, a church can deny them that ceremony from a religious standpoint. The issue is, no matter where you get married, a church, a garden, the beach, etc. you need a wedding license from the government for it to be recognized legally.
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The OP worded it terribly I recant my statement
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No worries.