Are these people opposed to all things artificial? Do they eschew wine made from grapes grown on grafted vines? Do they abstain from the use of optical prosthetics on the grounds that they are not natural? Do they harness a horse to a cart rather than employ an internal combustion engine or an electric motor? Do they carry their belongings on their heads rather than harness a horse to a cart? Do they refrain from opulent rituals on the basis of the artificial trappings of medieval bling? None of these things are considered "against nature" in the minds of these despots.
Margaret Sanger celebrated the fact that the Roman religion adopted the rhythm method as a birth control technique. It validated the essence of her mission. Romans claimed that the rhythm method did no violence against nature, but that other methods did. Why is one artificial means of contraception not against nature and all others are? It has something to do with the Roman hegemony over the definition of nature.
It could be said that there are two very distinct natures. One of them is under strict Roman control. The other is beyond the pale. One is a nature shrouded in darkness and the occult practices of Roman priests. The other nature is open and available to everyone outside of Roman control.
Yes, birth control techniques besides the rhythm method do violence to nature, but only the Roman nature. They do no violence to the other nature because the other nature does not exclude them. Yes, same-sex marriage is against nature, but only the Roman nature. The other nature does not exclude same-sex love.
Links: A Roman position on homosexuality and nature. A Roman position on contraception being against nature.