Say what you want, but I personally don't think it's insensitive to enjoy racist jokes (obviously depending on the approach).
However, there's absolutely, 100%, an appropriate time and place for them. He went about it in the wrong way, and on top of that, it wasn't even in good taste.
I don't think what he did was a big deal, but I myself would fire him. He knew he was representing Fox Sports when he did it, and that makes me think he's not all there in the head. There's no chance he thought, "these guys won't mind being associated with this."