The cooks can either butcher or make jerky but they always choose to butcher so then I have a lot of raw meat so people get sick or mad
Is hunting then grilling the only option for food early game?
I survived even on desert (haven't tried north pole yet), but I have failed few times before I succeed on that.
Tips: Camp fire (made out of kindling, in temperature tab) is great for early cooking. You can make there simple meals without the need of tableware, or cook fish/bake potatoe. All of these options are great.
As a source of food fishing is superb, as from hunting I couldn't survive very long as animals were running out on the desert too quickly. I was helping myself with shimmershrooms (they are great to eat as raw) - mine few blocks of any mountain and you should get some too. Make sure to disable it as an ingredient for cooking (shimmershroom), as it's better to eat as raw (and lasts fresh longer).
So there are few tricks to make cook prioritize cooking over butchering:
1) you can set range to get ingredients for recipe in bills - lower that to narrow area and set dumpling zone for animal corpses only nearby butchering table. This will make sure your cook won't go on the adventure to get some random corpses which happen to be all around the map, but wait for hunter to kill and carry them here
2) if you have too many corpses and he keeps butchering, you can always suspend the task for a while to make the cook focus on cooking
3) the ultimate solution is to have 2 people cooking: 1 butchering and 1 cooking