It's not good to assume all hope is lost, but it is also dangerous to bury your head in the sand.
Even if food production falls globally by 25% or so, any famines will be due to distribution, not lack of global food production.
If we really screw up, we may have famines similar to what was relatively common up to about 1980.
And why did we stop having them?
Once export bans become tit-for-tat (not dissimilar to the tit-for-tat export/import control bans between US-China right now), then some countries will be fine, and others will experience mass starvation. Global food production per capita only works if there is free trade of food.
However, should global food trade suddenly stop, I may be one of those starving.
Edit: just to be clear: Global refusal to trade food is extremely rare. What happens a lot more often, is that some country is unable to purchase food abroad due to either some blockade or lack of purchasing capacity.
Some people just want to watch the world burn