"It is not what goes into the mouth that defiles a person, but what comes out of the mouth; this defiles a person. What comes out of the mouth proceeds from the heart. For out of the heart come evil thoughts, murder, adultery, sexual immorality, theft, false witness, slander. These are the things that defile a person." (Matthew 15:11-20)
Heart matters become health matters. Defilement is less about hand washing, as mentioned in the passage, as it is about the great damage inflicted from within a person. If what was said about our condition is true, we are in desperate need of heart surgery, something or Someone to stop the bleeding.
At the cross God successfully dealt with the cancer of sin by the shedding of the blood of his own Son. His work of complete inward cleansing produces a very different flow of thought and behavior, enabling us to "pursue righteousness, faith, love, and peace, along with those who call on the Lord from a pure heart." (II Timothy 2:22)