Do you believe that Jesus was teaching about clean and unclean meats or about ceremonial washing?
"Are you also still without understanding? Do you not see that whatever goes into the mouth passes into the stomach and is expelled? But what comes out of the mouth proceeds from the heart, and this defiles a person.... These are what defile a person. But to eat with unwashed hands does not defile anyone." (Matt. 15:16-18,20)
Yes, the context was the washing of hands. But he's obviously not talking about hand-washing per se; he's talking about "defiled food" (which passes into the stomach and is expelled).
From a health perspective, eating "unclean foods" may well have been ill-advised -- there was a good chance of getting trichinosis from pork, and red tide could often poison shellfish, for example; but it is difficult to square such food safety issues with what Jesus actually said.
Jesus is pretty clear in saying that a person is not made unclean by what he eats; even pork or shellfish wouldn't defile him in God's eyes. It's what is already in a person's heart that defiles him.
One can also make a pretty good case that Peter's vision in Acts 10 is confirmation of this view; not to mention Paul's discussions of eating food sacrificed to idols.