The first amendment does not give you the right to a definition of a word. In fact, I would argue the first amendment actually precludes us from using religion as the basis for that definition, as far as the government is concerned.
That makes no sense. Government cannot fail to place a definition on who it issues a license to without violating someone's rights? You believe in the positive right to a marriage license?
Libertarians are supposed to believe that rights are negative in nature.
No. As citizens of this country, we are obligated to recognize that the laws of the land are valid (even the ones we don't like). There fore, if the government says marriage is z, y and z and I believe (as part of my religion) that it is a, b, and c then I either capitulate and believe x, y and z per the government rule of law or I will be punished by the rule of law and thus persecuted for my religious beliefs.
Example: As an employer I would be obligated to recognize that my employee is married to someone in contradiction to my beliefs and extend benefits (leave, health care, etc). If I don't, I can be punished with fines, jail time or both. My religious belief is that I the employee and spouse aren't truly married, but if I don't recognize their marriage as valid then I will be persecuted.
Now, that's a direct example but the indirect nature of the law applies as well. Those that adhere to the strictest sense of marriage are, as of today, forced to recognize that divorced couples that remarry other people are valid marriages even though they don't believe they are. If they were to stand up and say no, they would be persecuted.
So, no I don't think there is a positive or negative right to a marriage license. I think it is a social construct that, if regulated, results in religious persecution. However, if unregulated, it would fall under the jurisdiction of social groups (religions, families, organizations and the like) to regulate marriage as an institution and a ceremony as they see fit.