Theoretical computer science. It can be viewed as the study of "what things can be automated in principle", and if that is fully automated everything that can be already has been. A lot of exponential cliffs make automated computer search techniques not much further ahead compared to a computer-assisted human with 70 years of history.

Senator and congressman

Psychotherapy (and related work that benefits strongly from a perception by the client/user/etc. that the worker/provider is an empathetic peer)

Plumbers. There's an effect the name of which is escaping me now, which essentially says that the easiest things for humans are the hardest things for AI to learn, and vice versa. One of the first things humans learn is how to engage in fine motor movements to manipulate their environment. I think this will be one of the last things systems embedded with AI will be able to do, so professions like plumbers where you have to finagle around with physical objects will be the last to be automated away. Car mechanics and electricians are probably up there too, especially since with all of these there are aspects of adhering to some sort of regulatory code that could get in the way of AI autonomy, similar to how self-driving is constrained by regulation.

Priest. The concept of an automated, human-made machine religious worker would raise too many issues with the whole concept to be ever implemented.

What counts as feasibility? Technically ChatGPT could already do the job of US president (with someone to tell it what's happening, asking it what to legislate etc.) but it likely would do a shit job, which people know, hence haven't adopted it. Would it need to be plausibly electable to be feasibly automatable? If so, then president may well be it.

Reiki healers haha

Massage therapists