Sir William Blackstone, the British jurist who died two hundred and thirty-two years ago? Somehow I doubt he had strong opinions on the the Reconstruction Amendments or modern LGBT rights movements.
But George Washington and most if not ALL of the founders actively opposed gays in military service. Who influance the Founders on law? Blackstone. Who did Blackstone get his influance regarding law and governance? The Bible.
Natural Law=Law of Nature=Law of Nature's God. Who is Nature's God? The Judeo-Christian God. The Reconstruction Amendments were a recomfirmation of these rights. LGBT rights would've been anathema to them. They were trying to see people as individuals not groups. We're they perfect? No that's why those amendments were set in place to protect racial minorities.