Fart is mostly methane. There are lots of methane-rich environments on earth where organisms thrive.

Of course, organisms that convert methane to stuff we can process would go into overdrive and likely out-compete most of what we currently consider “life” — and the air is mostly inert nitrogen, so getting rid of THAT would have all sorts of consequences.

And methane is one of the worst greenhouse gases, so you could expect the earth to rapidly heat.

Since there would be no oxygen, you wouldn’t get combustion right away; eventually the atmosphere would either boil off, or the methane would break down into CO2, which would eventually be processed to release oxygen and sequester the carbon.

At which point, everything would go up in one big fireball.