Let's take a moment to see how much more clear some New Testament passages become, when we understand what "holy" and "profane" actually mean.
In the Gospels and Acts, the word "holy" is only used to describe nine perople or places: Jesus, the Holy Spirit, God, the city of Jerusalem, the Temple's Holy of Holies, the angels, the prophets (both of old, and John the Baptist), God's Law/covenant, and firstborn children. Notice that in none of these cases was the process of making the person or thing "holy" based upon their actions: in all cases, they were set apart for God's purposes before they were born.
But now that we understand this term "holy", we can better understand a number of Scriptures.
Do not give dogs what is holy, and do not throw your pearls before pigs, lest they trample them underfoot and turn to attack you. Matt 7:6
This verse creates a lot of confusion and even stress among some people. Jesus' "pearls before swine" comment seems to be saying that we shouldn't be evangelizing to the lost, right?
No, not at all. First of course you must understand the context. In this passage, Jesus is speaking to a gathering of Mosaic Jews, talking about how they had misinterpreted the Law, and that it was much harder than they originally thought to remain on the "pure" part of the cleanliness axis. But he also warns them to not give to dogs/swine things that were precious (pearls) and set apart for special use (holy).
So what He is saying is very specific: the Jews were not to be trying to give their Law (which was holy, or set apart, for their use) to those who were profane/common (the dogs/swine--Gentiles). He is doing no more or less than reaffirming that the Mosaic Covenant binds the Jews, not to the rest of us.
Now after we leave the Gospels/Acts, and start getting into the church era, we see a fascinating change: one more group has been added to the list of those who are "holy"--anyone who has faith in Christ. Those who have faith are those who were set apart from before time for Him.
In Romans, Paul goes to great effort to demonstrate two things: (1) those who were not set apart as holy (i.e., Gentiles) are not worthy to receive God; and (2) no one is on the 'pure' side of the cleanliness axis anyway. But then, after discussing salvation through faith, Paul exhorts us: "present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship." Paul is calling us to sacrifice ourselves, and see our bodies as set apart for God's purposes. What does this mean? Perhaps in Peter it is a bit more clear. Here, Peter points out that we are set apart to lead worship just as the Jewish priests had been--but our sacrifice is ourselves, rather than an animal.
Recall how the Jewish priests were 'set apart' to bring worship and sacrifices to God? Well, Paul and Peter are saying, now we have been set apart for God (mind, body, and Spirit). We are holy. But God still desires cleanliness/purity, even among those who are holy; so how do we achieve it? There is no more need for works of sacrifice, for Jesus performed the sacrifice! All that is left to sacrifice, they say, is to turn ourselves over to Him.
Likwise, in Corinthians, Paul says that since the Spirit indwells us, we are now holy/set apart, just as His Temple is set apart.
Perhaps nowhere in the New Testament is the relationship between holiness and cleanliness better demonstrated than Ephesians 1:3-10:
Blessed be the God and Father of our Lord Jesus Christ, who has blessed us in Christ with every spiritual blessing in the heavenly places, even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love he predestined us[a] for adoption as sons through Jesus Christ, according to the purpose of his will, to the praise of his glorious grace, with which he has blessed us in the Beloved. In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace, which he lavished upon us, in all wisdom and insight making known[b] to us the mystery of his will, according to his purpose, which he set forth in Christ as a plan for the fullness of time, to unite all things in him, things in heaven and things on earth.
Notice a few things here. First, we are "holy and blameless before him. In love he predestined us for adoption as sons through Jesus Christ, according to the purpose of his will". So you see that, just as in the rest of the Bible, our status as "holy" or "common" is not based upon us, but predestined by God before we even were born.
But also notice part two of the statement--we are made "holy" through this setting apart, but we are made "blameless" (i.e., clean/pure) because of "redemption through his blood...which he set forth in Christ".
So you see, we are set apart as holy because God called us before all time; we become blameless when we have faith in Christ's sacrifice.
[Side note: much of the Calvinist-Arminian debate is nullified here. Clearly and explicitly, we are told that our 'holiness' is determined before time and our 'blamelessness' or cleanliness is based upon our faith in the sacrifice of Christ. So really the only argument is: did God 'set apart' everyone and some choose to not become blameless (the Arminian stance); did God set apart only those whom He wanted, and compel them to have faith in Him while compelling the others not to do so (the Calvinist stance); or did He set apart His elect, and help them overcome the boundaries of their will to have the needed faith, and allow the others to choose cleanliness or pollution as they see fit (the Lutheran stance). It's all kind of silly, in the end. Clearly from the passage above, and the others before it, we are made holy or not holy based upon no choice of our own. God sets apart those whom He chooses, as is His right as the chooser. But also clearly, our purity/cleanliness before God is not forced upon us (or forcably kept from us), but is based upon our belief/faith in Christ's sacrifice.]
Notice also Colossians, in which we are again told that we are to be presented "holy AND blameless". Notice a repeating pattern here? It is because our holiness is one thing, and our blamelessness/cleanliness is the other axis.
2 Timothy 1:8-10is an interesting passage. In it, we are reminded that when we have a holy or set-apart calling, it is for God's purposes, not ours. Now let's think on this for a minute. What is 'set apart' about our callings from God? It is not just that we are called to be priests--many pagans have priests, so there is nothing 'set apart' or different about that. No, it is that we are all called and set apart in whatever role we are called. I am an engineering manager. There are many engineering managers. But I have been set apart to be a holy engineering manager - to walk with Jesus every day in my role, so that I may be a priest to Him, not just someone balancing statics moments or troubleshooting chemistry/physics issues.
In many ways, we modern Christians have missed some of the glorious brilliance of our Scriptures, because we did not understand this concept of holiness. We confuse "holy" with "righteous", when they are two separate things: holiness is being set aside (not of your works, but at your birth) for a special purpose for God, dedicated to His purpose; righteousness is being clean or pure based upon your actions.
But because we read these two words as being synonymns, too often do we misinterpret what God is trying to tell us in His word. Instead, it is critical that we understand what holiness is, and what cleanliness/purity is. Hopefully this article helps with that.