How do Lutherans interpret Matthew 15:11? "What goes into someone's mouth does not defile them, but what comes out of their mouth, that is what defiles them." Matthew 15:11.
I guess one thing that Jesus wants to say here is that eating pork does not defile man, or any other food that was forbidden. But what else does Jesus mean? What about the "but what comes out of their mouth, that is what defiles them." part?
In Matthew 15:11, Jesus was responding to the Pharisees who said:


  "Why do your disciples break the tradition of the elders? For they do not wash their hands when they eat." - Matthew 15:2 ESV


Jesus replied:


  He answered them, "And why do you break the commandment of God for the sake of your tradition? - Matthew 15:3 ESV


Jesus was telling the Pharisees that they were treating their tradition as equal to or greater than God's law.  Thus:


  10 And he called the people to him and said to them, "Hear and understand:
  11 it is not what goes into the mouth that defiles a person, but what comes out of the mouth; this defiles a person." - Matthew 15:10-11 ESV


He later elaborates that:


  17 Do you not see that whatever goes into the mouth passes into the stomach and is expelled?
  18 But what comes out of the mouth proceeds from the heart, and this defiles a person.
  19 For out of the heart come evil thoughts, murder, adultery, sexual immorality, theft, false witness, slander.
  20 These are what defile a person. But to eat with unwashed hands does not defile anyone." - Matthew 15:17-20 ESV


Put another way, your evil actions toward God and toward others are the source of your sin, not the failure to practice church rituals.