I'm not asking if it should be illegal, though that's a fairly connected question. I'm not asking, either, per today's Supreme Court hearing, if it's unconstitutional, or if it should be.
I'm asking if, at least in certain circumstances, it is currently illegal.
What makes me say that?
In a word, HIPAA. Specifically, the privacy rule part of the Health Insurance Portability and Accountability Act. Given the "immortal cells" of Henrietta Lacks and many other hypercapitalism-driven invasions of our genetic privacy, I'd argue that the default position behind the idea of gene patenting violates HIPAA, and that, therefore, some sort of "prior restraint" applies.
You'll never get today's Supreme Court, and probably not any lesser-level federal court, to follow such a line of reasoning.
Too bad. I think it's very strong.
Per the HHS summary of who is covered, I think it applies.