Matthew 7:5 Thou hypocrite, first cast out the beam out of thine own eye; and then shalt thou see clearly to cast out the mote out of thy brother's eye. 6 Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you.
There is an analogy about the dog in Proverbs 26:10 The great God that formed all things both rewardeth the fool, and rewardeth transgressors. 11 As a dog returneth to his vomit, so a fool returneth to his folly. 12 Seest thou a man wise in his own conceit? there is more hope of a fool than of him.
There is a dual reference to both dog and swine in 2 Peter 2:21 For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them. 22 But it is happened unto them according to the true proverb, The dog is turned to his own vomit again; and the sow that was washed to her wallowing in the mire.
These verses all tie together as judging others or another word using discernment within those we take the Gospel to that need to hear it. The terms dog and pigs are an analogy of those who reject the Gospel after hearing it as they trample it and return back to their evil ways. It's the same with hypocrites as they love to judge others, but yet also trample the Gospels and return to their own conceits.
Matthew 10:14 And whosoever shall not receive you, nor hear your words, when ye depart out of that house or city, shake off the dust of your feet.
If the dogs and swine (people) refuse to listen to the Gospel being preached to them then don't judge them, but walk away from them as they will never receive it as it is already discerned in their rejection and the fool (one who rejects) and transgressor (conceited hypocrite) already have their reward being already judged by God.