These two things are in conflict. We could ignore both asteroids and climate change and according to the best known science there'd be very little impact for vast timespans and possibly no impact ever (before humanity is ended by something else like war).
Yes, also for the climate. Look at the actual predictions and it's like a small reduction in GDP growth spread over a very long period of time, and that's assuming the predictions are actually correct when they have a long track record of being not so.
Really stuff like asteroids and climate is a good counter-argument to caring about AI risk. Intellectuals like to hypothesize world-ending cataclysms that only their far sighted expertise can prevent, but whenever these people's predictions get tested against something concrete they seem to invariably end up being wrong. Our society rewards catastrophising far too generously and penalizes being wrong far too little, especially for academics, NGOs etc. It makes people feel or seem smart in the moment, and they can punt the reputational damage from being wrong far into the future (and then pretend they never made those predictions at all or there were mitigating factors).