A few points on this:
When the Torah uses the word Toevah in reference to the lifestyle, it only refers to men. Women have a separate issur. The main difference is that for women I don’t believe there is a death penalty, and it’s definitely not yehareg v’al yaavor.
Aveirah says that being mechalel Shabbos doesn’t go against the essence of a person. True, because Shabbos isn’t something that relates to a person. But it does relate to creation. We say in Friday night’s davening that Shabbos is the tachlis of creation. The entire creation relies on Shabbos – I’d say that violating it would go against the normal fabric of things, just as homosexuality does.
The world was built on truth. I’m sure we all know it says that Emes is the foundation. Cheating in business is the opposite of that. Again, it’s something that goes against the very essence of the world and creation.