No rights are "inalienable," that is, handed down by God or Nature. The only law handed down by Nature is the law of the jungle, where the strong eat the weak. Every right was wrested by people, after long and bloody struggles, from their reluctant rulers.
Think about this -- if gun rights are "inalienable" and inherent, then we don't have to lift a finger to protect them. This is a poor basis upon which to mobilize pro-gun activism. It just gives gun owners an excuse to do nothing.
Further, if rights are "inalienable," there would be no need for a Bill of Rights. They would just be there, in the ether. And, "inalienable" rights would be universal, throughout the world. Show me any other advanced country that has gun rights on the scale of the U.S.
Yes, there is prattle about "inalienable rights" in the Declaration of Independence. The author, Thomas Jefferson, besides being a world-class hypocrite regarding his slaves, was a very clever 18th century propagandist. Just remember that the Declaration (unlike the Constitution) is not legally binding. Zero actual force and effect. Think of it as poetry. The verbiage doesn't stand the test of logic.