If geothermal isn't renewable, then neither is solar. Or wind. Or hydro. Those all trace to irreversable conversion of hydrogen to helium. Geothermal comes from fission, just like nuclear.

Geothermal does not come from fission. It comes from some combination of primordial heat (which is gravitational), and alpha and beta decay (not fission).

I had gathered that primordial heat would have petered out billions of years ago. That the radioactive decay cited as providing long-term heat is not primarily fission is a surprise. But isn't alpha decay really a kind of fission? It's not useful for chain reactions, but that's a whole other topic.

No, alpha decay is a distinct nuclear process.