I think Matthew 7:6 adds support to a previous post where I argued for an nontraditional understanding of "salt of the earth" (Matthew 5:13). Matthew 7:6 speaks of pigs trampling the disciples' "holy things" and then turning to attack the disciples themselves. In the post titled "Disciples: Salt for Trampling," I proposed that "salt of the earth" signifies the way outsiders treat the disciples. Those who follow Jesus have broken ties with the kingdom of earth, they've lost their saltiness. They are good for nothing but trampling (καταπατεω) under foot. To paraphrase 5:13 in the context,
The values of the kingdom of God (vv 3-12) are so different than those of the world that disciples of Jesus can expect to be "trampled under foot," (v 13). To the world, they are nothing but useless salt. Nevertheless, good deeds done on behalf of Jesus point beyond themselves. So, let your light shine (v 14-16).
In Matthew 7:6 both the things being trampled and torn (καταπατεω, ρηγνυμι) and the context are clear. The pigs lash out at the disciples because they have no regard for their holy things. These are a couple of most obscure passages in the New Testament, but I think it is reasonable to understand the object of the violent activity in both passages as persecuted followers of Jesus.