If the entire world went to zero carbon emissions tomorrow, the effects would still be serious. Given that's not going to happen, the effects are likely to be catastrophic.

You're right that it won't mean the extinction of life on earth or humanity, but it might turn out to be the end of advanced human civilization if the bad end of the predictions come to pass. If there's not enough arable land left to support the human population, things will get very ugly very quickly.