In prep for a previous campaign I looked into what alternatives there might be to hemoglobin. It brought me here:
https://worldbuilding.stackexchange....rs/28380#28380 and if you scroll down far enough you'll find reference to the easily pronounceable "Chloro-carbonyl-bis(tri phenylphosphine)-iridium", which would allow the blood to transport both oxygen and hydrogen.
I imagine that this could of course give you a species that lives on a planet with free hydrogen but no free oxygen, though I have no idea how you'd keep the supply of hydrogen in the air. I suppose the plant analogues could breakdown free hydrocarbons (A stand-in for CO2) into carbon and hydrogen, but as far as I know that generally requires oxygen involved in the process somewhere and the result is H2O, not free hydrogen. At which point you'd need to find some way to split the hydrogen and oxygen, which is a process that costs energy, rather than supplying it.
Maybe I should have paid more attention in chemistry class, but in any case, you have an example of a way to metabolize something other than oxygen.