How do the proponents of the doctrine that salvation can't be lost usually explain Matthew 7:21-23?

Scripture answers scripture. See John 6:43-48, & 6:64-70. And so many more. Look at 11 Thess 2:13 & 14. It is not what I think, but what the Word of God teaches. "Now unto him who is able to keep you from falling and present you faultless before the presence of his glory with exceeding joy. To the only wise God our Saviour, be glory and majesty, dominion and power, forever, amen. Jude 24 & 25

I posted this answer to this question on a duplicate question that will likely be closed I'm reproducing my answer here:

Jesus lived prior to the giving of the gospel of the grace of God and the formation of the new human (the body of the Christ) which would not arrive until Paul, the architect was commissioned by Christ in Acts 9ff. Jesus did not live in the current age but rather at the end of the previous age:

ESV Matthew 24:3 As he sat on the Mount of Olives, the disciples came to him privately, saying, “Tell us, when will these things be, and what will be the sign of your coming and of the end of the age?

ESV Hebrews 9:26 for then he would have had to suffer repeatedly since the foundation of the world. But as it is, he has appeared once for all at the end of the ages to put away sin by the sacrifice of himself.

ESV Acts 2:

16 No, this is what was spoken by the prophet Joel: 17 “‘And in the last days it shall be, God declares, that I will pour out my Spirit on all flesh, and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams;

ESV Hebrews 1:2 but in these last days he has spoken to us by his Son, whom he appointed the heir of all things, through whom also he created the world.

ESV 1 Corinthians 10:11 Now these things happened to them as an example, but they were written down for our instruction, on whom the end of the ages has come.

ESV 1 Corinthians 3:10 According to the grace of God given to me, like a skilled master builder I laid a foundation, and someone else is building upon it. Let each one take care how he builds upon it.

ESV Ephesians 1:

7In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace, 8which he lavished upon us, in all wisdom and insight 9making known to us the mystery of his will, according to his purpose, which he set forth in Christ 10as a plan for the fullness of time, to unite all things in him, things in heaven and things on earth.

ESV Galatians 4:4 But when the fullness of time had come, God sent forth his Son, born of woman, born under the law,

ESV Matthew 10:23 When they persecute you in one town, flee to the next, for truly, I say to you, you will not have gone through all the towns of Israel before the Son of Man comes.

ESV Matthew 24:34 Truly, I say to you, this generation will not pass away until all these things take place.

ESV Matthew 23:36 Truly I tell you, all these things will come upon this generation.

ESV Luke 11:

29When the crowds were increasing, he began to say, “This generation is an evil generation. It seeks for a sign, but no sign will be given to it except the sign of Jonah. 30For as Jonah became a sign to the people of Nineveh, so will the Son of Man be to this generation. (resurrection)

To him would be committed the gospel and the 7 mysteries of the new dispensation:

https://biblehub.com/topical/d/dispensation.htm

In the meantime Jesus was "born under the law" and was not sent to upend the Torah, mikveh (aka "baptism") and conditional salvation:

ESV Galatians 4:4 But when the fullness of time had come, God sent forth his Son, born of woman, born under the law

ESV Matthew 5:17 “Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them.

(Or possibly as the NLT has it):

NLT Matthew 5:17 "Don't misunderstand why I have come. I did not come to abolish the law of Moses or the writings of the prophets. No, I came to accomplish their purpose.

He is not concerned with personal justification by faith alone but rather with the arrival of the kingdom of God (glorified Israel), of which he spoke endlessly. Entrance into the kingdom of God was conditioned on repentance, obedience to Torah, mikveh (water "baptism") and so on:

ESV Matthew 7:

21“Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven. 22On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?’ 23And then will I declare to them, ‘I never knew you; depart from me, you workers of lawlessness.’

It was essential to believe that Jesus was the Messiah but that was not enough. Just recognizing him as the Messiah (addressing him as KURIE, KURIE) was not sufficient apart from meeting the conditions of repentance, obedience to Torah, mikveh and the like. Faith without works (in the previous age) is dead.

I am currently researching the timing of the new covenant and the baptism of holy spirit and how it all works together, and have been for some time but it appears that the remnant were "born of the spirit" and had the law written on their hearts and were provided with everything that they needed to actually fulfill the righteous requirements to be prepared while the leaders were hardened (in order to bring in the gentiles (Romans 11:26)). But being born again and having holy spirit was not a guarantee. Endurance was:

ESV 1 John 5:

16If you see any brother or sister commit a sin that does not lead to death, you should pray and God will give them life. I refer to those whose sin does not lead to death. There is a sin that leads to death. I am not saying that you should pray about that. 17All wrongdoing is sin, and there is sin that does not lead to death. 18We know that anyone born of God does not continue to sin; the One who was born of God keeps them safe, and the evil one cannot harm them.

ESV 2 Peter 1:

3His divine power has granted to us all things that pertain to life and godliness, through the knowledge of him who called us toc his own glory and excellence,d 4by which he has granted to us his precious and very great promises, so that through them you may become partakers of the divine nature, having escaped from the corruption that is in the world because of sinful desire. 5For this very reason, make every effort to supplement your faith with virtue,e and virtue with knowledge, 6and knowledge with self-control, and self-control with steadfastness, and steadfastness with godliness, 7and godliness with brotherly affection, and brotherly affection with love. 8For if these qualitiesf are yours and are increasing, they keep you from being ineffective or unfruitful in the knowledge of our Lord Jesus Christ. 9For whoever lacks these qualities is so nearsighted that he is blind, having forgotten that he was cleansed [in mikveh] from his former sins. 10Therefore, brothers, be all the more diligent to confirm your calling and election, for if you practice these qualities you will never fall. 11For in this way there will be richly provided for you an entrance into the eternal kingdom of our Lord and Savior Jesus Christ.

ESV Hebrews 10:

24And let us consider how to stir up one another to love and good works, 25not neglecting to meet together, as is the habit of some, but encouraging one another, and all the more as you see the Day drawing near. 26For if we go on sinning deliberately after receiving the knowledge of the truth, there no longer remains a sacrifice for sins, 27but a fearful expectation of judgment, and a fury of fire that will consume the adversaries. 28Anyone who has set aside the law of Moses dies without mercy on the evidence of two or three witnesses. 29How much worse punishment, do you think, will be deserved by the one who has trampled underfoot the Son of God, and has profaned the blood of the covenant by which he was sanctified, and has outraged the Spirit of grace? 30For we know him who said, “Vengeance is mine; I will repay.” And again, “The Lord will judge his people.” 31It is a fearful thing to fall into the hands of the living God.

This is not Paul's gospel ("the gospel of the grace of God") but rather the gospel of the last days of the Jewish covenant(s).

In Paul's gospel justification is a gift, apart from any kind of personal accomplishment.

ESV Eph 2:

4But God, being rich in mercy, because of the great love with which he loved us, 5even when we were dead in our trespasses, made us alive together with Christ—by grace you have been saved— 6and raised us up with him and seated us with him in the heavenly places in Christ Jesus, 7so that in the coming ages he might show the immeasurable riches of his grace in kindness toward us in Christ Jesus. 8For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, 9not a result of works, so that no one may boast.

In Paul's gospel there is no dependence on the Torah and its religious activities or any other effort. A gift does not involve effort.

Rather than being judged at some future date, the believer is immediately transferred into the kingdom of God's dear son:

ESV Eph 1:

11In him we have obtained an inheritance, having been predestined according to the purpose of him who works all things according to the counsel of his will, 12so that we who were the first to hope in Christ might be to the praise of his glory. 13In him you also, when you heard the word of truth, the gospel of your salvation, and believed in him, were sealed with the promised Holy Spirit, 14who is the guarantee of our inheritance until we acquire possession of it, to the praise of his glory.

ESV Colossians 1:

12giving thanks to the Father, who has qualified you to share in the inheritance of the saints in light. 13He has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son, 14in whom we have redemption, the forgiveness of sins.

So in order to correctly apply the scriptures to the current age one must not build one's hope on the conditional promises to be found righteous and enter the kingdom of God in the last day but rather on the operation of God through faith alone. In this age it is God that justifies based on the propitiation God provided in Christ's blood:

ESV Romans 5:19 For as by the one man’s disobedience the many were made sinners, so by the one man’s obedience the many will be made righteous.

Church pews are filled with people who profess to know the Christ, but do not live the kind of life Jesus indicated we should. Those are the ones Jesus is referring to here.

All too often people miss the point of Jesus parable of the sower.

Mat 13:18 through 22 KJV  Hear ye therefore the parable of the sower. When any one heareth the word of the kingdom, and understandeth it not, then cometh the wicked one, and catcheth away that which was sown in his heart. This is he which received seed by the way side. But he that received the seed into stony places, the same is he that heareth the word, and anon with joy receiveth it; Yet hath he not root in himself, but dureth for a while: for when tribulation or persecution ariseth because of the word, by and by he is offended. He also that received seed among the thorns is he that heareth the word; and the care of this world, and the deceitfulness of riches, choke the word, and he becometh unfruitful.

Many of those who fit well into those descriptions are in Church every Sunday.

Even the Apostle Paul was hoping for his salvation, not necessarily assured of it. It is one thing to study Scripture and believe that according to its own requirements (i.e. they that call upon the name of the Lord shall be saved) one is saved, and quite another to know this within oneself.

It is also another thing to discuss how one actually views salvation. Is it being lost with God or being lost without God?

As for your example from Matthew, it is a thorny one. However, it can be answered with a schoolroom example. Did you ever have a friend who stood by you even when doing so was inconvenient and the friendship was paying very little in dividends? Then there is another kind of friend. It is one who uses his(her) friendship with you for gain in others areas of life. This kind of friend is unlikely to be intimate with you and ask your advice about how to use his friendship with you. That person has only his or her personal agenda uppermost in mind. So even though they used their association with you for gain, they never KNEW you.

Perhaps this is helpful.

There are several perceived difficulties with this passage.

1. Equating entering the kingdom with salvation.
2. Equating saying "Lord, Lord" with salvation.
3. Equating casting out devils as proof of salvation.

Let's address each one.

1. Paul wrote to the church saying that the immoral shall not inherit the kingdom of God (Galatians 5:19-21. So it is possible that the church (composed of saved people), can be saved and miss out on receiving glory in the coming kingdom. They will be excluded from honor in the kingdom and will not reign with Christ in it. This part of salvation can be lost without losing other aspects of our salvation. For instance, Romans 8:32-39 is emphatic that those who live according to the Spirit will never be "separated from the love of God." They will be in the new heavens and new earth, but not in the kingdom with honor. For more on this, see Paul N. Benware, The Believer's Payday.

2. Just calling Jesus "Lord" does not mean that one actually lives with the sense of yielding to Christ's authority in life and conduct. "Lord" may be a title more than a position of honor for some people. This is just common sense.

3. Judas cast out devils and performed miracles with the other disciples when they went out two by two. Was he saved? Can one be used by God and still be a nominal Christian? Yes; God may use any instrument He wishes, even to borrow the tongue of a donkey as He did in the OT.