There are different meanings to natural law. Humans are meant to follow a natural law that has choice embedded in it - God given free will. I’m not referring to anything Darwinist or based on evolution theories.
Animals do not have the choice, that free will.
Marriage has always and will always mean a man and a woman. Some cultures, religions and times have permitted polygamy, but that is still man+woman.
It has never been and will never be man+man or woman+woman or any other sicko combination. If humans pretend it means that, they may play at that for a short while, but it is foolish, insane and against both the law of nature in the cells, and the law of nature inscribed in everyones’ hearts, by God.
"If there is no natural right, no natural family, no ways of God reflected in the nature of mankind, then there are no unalienable rights; no principle of justice that requires their security; no authoritative basis for the rightness of government based on consent; no claim to self-government, of, by and for the people."-- Alan Keyes, August 26, 2010