I'm creeped out about having to pick up a dead opossum
Why are dead animals weird to you?
There are lots of reasons, I'm having lots of fears, thinking about the unpleasant smells.
That definitely is gross, but picking up roadkill is still your duty and you need to do it no matter how you feel. If the roads were filled with roadkill, then it would be dangerous and disgusting to drive around.
I still don't want to do it.
I think you should look for another job. There is nothing wrong with admitting you're not right for it and finding something that suits you better.