There’s a very long history to the idea of a mind disconnected from the sexed body. That’s why the “gendered soul” concept could get so far so fast, because it’s not exactly a departure from the old dualism, which saw the body as a mere vessel for the immortal, all-important soul. It’s not even a particularly western concept, see also reincarnation.

So I think you’re right in seeing a connection between the dualistic thinking and trans-nonsense, it’s just that I don’t think it’s in any way particular to either Obama or even to trans-nonsense. I think it’s rather a strong undercurrent in human culture, which has been embraced and used by the trans ideologists.

If you think about it, the idea that a person is not their body, or that they are something more, something else than their body, is actually everywhere. Trans is just one of the more extreme manifestations of it.