Can Sarah Palin be Denied a Hunting License Based on Religious Beliefs?

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For the sake of debate and my own law school education process, let's change the facts of the Kentucky clerk case around a bit and see if that changes your opinion.

What if an Inuit clerk in Alaska refuses to issue a hunting license to Sarah Palin because she is a woman? His reason is his religion says only men are allowed to hunt. Using the precedent set by the Kentucky clerk if she were to prevail, would that be acceptable? Would forcing him to issue a hunting license to Sarah Palin violate his 1st amendment rights?

If the answer is yes: Does his 1st amendment right trump Sarah Palin's 2nd amendment right, as well as her 14th amendment right to equal protection under the law? Would liberals view this situation differently? How about conservatives? Replace the Inuit clerk with a Muslim clerk; or what if she was applying for a concealed carry permit and a clerk had a religious objection? Does that change your view?

Does this scenario make you friendlier to the idea of keeping church and state separate?