In Matthew 7:6, Jesus says, "Do not give dogs what is holy, and do not throw your pearls before pigs." Here we have some practical advice in witnessing and reproving. Since I began witnessing, my personal prayer has been for God to consume me with zeal for the glory of Jesus Christ. I believe such zeal will overcome the many fears and inhibitions that prevent so many from being an effective witness. But here Jesus warns us to let our zeal be guided by discretion, "lest they trample them underfoot and turn to attack you."
Notice that the gospel or the reproof is a holy thing, a pearl. A wise man will see it so and welcome it.

Like a gold ring or an ornament of gold
is a wise reprover to a listening ear.
Proverbs 25:12

Let a righteous man strike me—it is a kindness;
let him rebuke me—it is oil for my head;
let my head not refuse it.
Psalm 141:5

[Wisdom] is a tree of life to those who lay hold of her;
those who hold her fast are called blessed.
Proverbs 3:18

Doctrine should be held in the highest estimation.
But there are dogs and pigs in this world. Remember, dogs and pigs were unclean animals. Does this mean that we should not share the gospel with wicked and profane people, then? Of course we should. Jesus said to, “Go into all the world and proclaim the gospel to the whole creation." (Mark 16:15) Paul said that "we are the aroma of Christ to God among those who are being saved and among those who are perishing, to one a fragrance from death to death, to the other a fragrance from life to life." (2 Corinthians 2:15, 16)
In fact, only in preaching to them, will you discover the dogs and pigs. I see two ways God has given us for detecting dogs and pigs. One is to share the gospel with them. You cannot know if someone is a child of God or a pig, so you must present the gospel to everyone indiscriminately. Do not judge on appearances. If you have truly preached to them sin, righteousness, and judgment and they stubbornly blaspheme the gospel, even persecuting you, you have probably discovered a dog or pig.
I see the other method for detection in church discipline. Perhaps like Bill O'Reilly, you're not familiar with this essential passage. It is Matthew 18:15-20:

“If your brother sins against you, go and tell him his fault, between you and him alone. If he listens to you, you have gained your brother. But if he does not listen, take one or two others along with you, that every charge may be established by the evidence of two or three witnesses. If he refuses to listen to them, tell it to the church. And if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector. Truly, I say to you, whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven. Again I say to you, if two of you agree on earth about anything they ask, it will be done for them by my Father in heaven. For where two or three are gathered in my name, there am I among them.”

By these two methods, you can discover dogs and pigs. By walking so long in the counsel of the wicked, taking their stand in the way of sinners, and sitting with the scoffers, they have hardened their hearts. "The dog returns to its own vomit, and the sow, after washing herself, returns to wallow in the mire." (2 Peter 2:22)
Do not waste your time or your holy words on them. “It is not right to take the children's bread and throw it to the dogs.” (Matthew 15:26)

“‘Look, you scoffers,
be astounded and perish;
for I am doing a work in your days,
a work that you will not believe, even if one tells it to you.’”
Acts 13:41

As the prophet said to King Amaziah, "I know that God has determined to destroy you, because you have done this and have not listened to my counsel.” (2 Chronicles 25:16b)
Notice also in this passage the love of Jesus for his sheep. By his own admission, he has sent us out as sheep in the midst of wolves. Persecution will come. But he warns us, so we do not seek persecution by our zeal for his glory.

From oppression and violence he redeems their life,
and precious is their blood in his sight.
Psalm 72:14