There are ethical issues around mass-exterminations of species, but the earth as a system will be fine. To quote a New Model Army song, "She'll survive us all perfectly well when we're all long buried and dead."

Humans will have problems, though. Expect significant issues around a whole range of topics - from water to refugees - to increase dramatically. And I don't think it's impossible that democracies and democratic notions end up taking a bit of a battering in the medium term.