Here’s a full transcript of the monologue - which is absurdly hard to find in all the coverage.
By design. If it was actually offensive Fox would be playing it non-stop. The offense has been excavated from inside an implication of a phrase in a nested clause in a sentence saying something unrelated.
Kimmel said (as part of an argument that republicans were playing politics by pointing fingers) that republicans were trying to prove that Robinson was not a republican , from which you have to infer that Kimmel meant to say Robinson was a republican.
Nobody checks what he actually said, they're just angry because they were told to be angry.