There are only seven uses of the Greek word anenklētos (blameless, above reproach, irreproachable) in the New Testament.

Three of these uses refer to one of the requirements of an elder (1 Tim 3:2; Titus 1:6) or a deacon (1 Tim 3:10). Those are fairly well known. The other four are not so well known.

One refers to widows:

Honor widows who are really widows. But if any widow has children or grandchildren, let them first learn to show piety at home and to repay their parents; for this is good and acceptable before God. Now she who is really a widow, and left alone, trusts in God and continues in supplications and prayers night and day. But she who lives in pleasure is dead while she lives. And these things command, that they may be blameless. But if anyone does not provide for his own, and especially for those of his household, he has denied the faith and is worse than an unbeliever (1 Tim 5:3-8, emphasis added).

So not only should elders and deacons in the local church be blameless/above reproach, but so should widows. In light of this surely all in the local church should be blameless. The elders and deacons are to be examples of what the whole flock should be like.

The final three uses of anenklētos show that the aim of every believer is to be found blameless at the Judgment Seat of Christ.

First, Paul prayed for the believers in Corinth “that [they] may be blameless in the day of our Lord Jesus Christ” (1 Cor 1:8). The expression the day of our Lord Jesus Christ refers to the Judgment Seat of Christ (the Bema) in the Corinthian letters (compare 1 Cor 3:13; 4:3; 5:5; 2 Cor 1:14) and in several of Paul’s other letters as well (compare Phil 1:6, 10; 2:16; 2 Tim 1:12; 4:8).

Second, Col 1:22 is often cited as teaching the Reformed Doctrine of the Perseverance of the Saints. Yet it actually teaches the doctrine of eternal rewards for believers who persevere and hence will be found blameless at the Bema:

And you, who once were alienated and enemies in your mind by wicked works, yet now He has reconciled in the body of His flesh through death, to present you holy, and blameless [amōmos], and above reproach [anenklētos] in His sight—if indeed you continue in the faith, grounded and steadfast, and are not moved away from the hope of the gospel which you heard… (Col 1:21-23, emphasis added).

If we simply look at the other six uses of anenklētos in the NT, it is clear what Paul means here. He is not warning believers that if they fail to persevere they will prove they were false professors and will end up in the lake of fire. He is encouraging believers to persevere so that they may be presented by Christ at the Bema as having been holy, blameless, and above reproach in this life.

Third, in 1 Tim 6:13-14 Paul urges Timothy, obviously a born-again and eternally-secure man, to persevere so that he might be highly rewarded at the Bema:

I urge you in the sight of God who gives life to all things, and before Christ Jesus who witnessed the good confession before Pontius Pilate, that you keep this commandment without spot, blameless [anenklētos] until our Lord Jesus Christ’s appearing… (emphasis added).

Blamelessness in the NT is not sinlessness. It means to be one who is an exemplary Christian, one who will be approved by Christ and praised by Him at the Bema (cf. Luke 19:17). Not all believers are blameless all the time. But we can and should be. That is our calling. We should long to be found blameless by Him. A simple word study plainly reveals this, even to a math professor.