Separation of church and state means the US state can’t establish or sanction an official state religious institution (like the Church of England). Whether individual laws or lawmakers are inspired by Locke, Rousseau, Marx, Chomsky, Ann Coulter, the New Testament, the Quran, or any other source has no relation to that, and doesn’t equate to official state endorsement of any institution.
Every law or policy has to be based on some philosophical backdrop. Being from a religious source (ie Christian) is not inherently less valid than any other source, constitutionally speaking. The distinctions of validity are only on the basis of individual or social bias, and that’s the basis of public debate.
The civil recognition of marriage is obviously a product of Christian society, which people can oppose, but invoking separation of church and state can’t be used as an argument against that. A government marriage document is not a state recognition of any particular church or institution, or creating a “Church of America”.