In 1 Peter 1:22, Peter writes,

“Having purified your souls by your obedience to the truth for a sincere brotherly love,
love one another earnestly from a pure heart.”

Today I have been focused on the phrase “having purified your souls by your obedience to the truth.” Bible scholars disagree on what this means. Some believe this “obedience to the truth” refers to faith in the Gospel and thus the purification of one’s soul refers to justification and salvation. Others understand the purification to refer to the removal of sin from the inner man as a result of obedience. Which one does Peter mean and why does it matter?

First, it is important to point out that both of these possible meanings are generally biblical. In other words, we know that God purifies our souls based on our faith in the Gospel (1 Cor 6:11 - just as we are sanctified and justified). We also know that as Christians we should choose to purify our bodies and souls by removing sin from our lives (2 Cor 7:1).

So which meaning does Peter intend in 1 Peter 1:22? Here are the reasons that I believe Peter is talking about the removal of sin from the Christian’s life.

This seems to me to be the most natural and straightforward reading.
The only other two appearances of the word translated “purified” (hegnikotes) in the NT (James 4:8; 1 John 3:3) definitely refer to the cleansing of a Christian’s life from sin.
Here the purification is done by the Christian, not by God. Generally, if not exclusively, the cleansing of a person at salvation is described as something that God does.
While it is possible to refer to faith in the gospel as “the obedience of faith” (Rom 1:5; 15:18), the normal use of “obedience” in the NT refers to holy living.
The main idea of the preceding section of Scripture (1 Peter 1:13-20) is a call to live a holy life.
The imperative of this verse is to “love one another earnestly from a pure heart.” Just as believers are responsible for loving “earnestly,” they are also responsible for loving “from a pure heart.” This is not referring to justification, but to their choice to be holy in their hearts.
The next section, 1 Peter 2:1-3, explain the application of this verse: “So put away all malice and all deceit and hypocrisy and envy and all slander.” These, of course, are issues of holiness in the inner man that would be the basis for loving from a pure heart.

In view of 1 Peter 2:1-3, we are able to discover the importance of inner holiness for loving others. The sins of our heart (or soul/inner man) are what hinders us from loving others. As Peter mentions, these include malice, deceit, hypocrisy, envy, and slander. When we are struggling to love others like God has called us to, then an important step to take, as Peter teaches here, is to remove the sin from our inner selves (purify our souls) in obedience to the truth. Then we are in a great position to “love one another earnestly from a pure heart”!

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[Added on April 14, 2018]

A friend asked me if the past tense of "purified" doesn't support the interpretation that the phrase "having purified your souls" refers to conversion.

This past tense is a perfect, which conveys the idea of a completed act that has ongoing results. Here is how a perfect tense fits into my suggested interpretation that the purification of our souls by obedience to the truth means that we are responsible for removing sin from our lives.

Even though this is something that we may do on an ongoing basis in our Christian life, that is not to say that a Christian cannot remove all known sin from their lives at any given point in time. For example, in James 4:8 Christians are commanded to purify their hearts. I think we should assume that this is possible to do (complete), not just something you are always doing.
This does not necessarily mean that a Christian who purifies their heart is therefore free from all sin. This is because there may be sin in his life that he is not yet aware of. God is gentle and faithful to give us what we can deal with. We can have a pure heart to the extent that we have confessed and repented of all known sin of the inner man.
A good example of a similar use of a past tense is Ephesians 4:25: “Therefore, having put away (aorist participle) falsehood, let each one of you speak the truth with his neighbor.” This doesn’t mean it may not have to be done again. It just indicates that something has to be and can be done in order to accomplish something else.