[Sir Francis Dashwood]

Legally, marriage in America is not inherently a religious institution.

Wrong... Monogamy is a religious institution.

Directly from Reynolds...

"So here, as a law of the organization of society under the exclusive dominion of the United States, it is provided that plural marriages shall not be allowed. Can a man excuse his practices to the contrary because of his religious belief? [98 U.S. 145, 167] To permit this would be to make the professed doctrines of religious belief superior to the law of the land, and in effect to permit every citizen to become a law unto himself."

[steve-b]

Nope. The decision says precisely the opposite — that monogamy is a civil institution which may not be superceded by religious doctrine.