Everything an unbeliever does is sinful, right? (Heb 11:6).

An unbeliever's "prayers", "seeking", "repentance" and "turning from sin" -- all these things are sin (Rom 10:14). In fact, all their feelings of "remorse", "regret", "guilt", "sorrow" must be sin. Any attempt to be "humble" or "sincerely turn from sin", is in fact sin. Because all the unbeliever's works are works of unbelief. If they try to be sincerely "seeking salvation", it's because they don't think Christ was sincere enough. By "seeking faith in order to be saved", an unbeliever shows they think they are capable to "finishing off" what Christ "failed" to do.

Scary, huh? Especially when you hear ministers (not of Christ) telling unbelievers to pray. Because everything an unbeliever does is sin, that means that praying will only serve to increase the unbeliever's sin (condemnation). In fact, every attempt by an unbeliever to "stop sinning" only increases their condemnation.

Take for example an unbeliever called John. Now, imagine a preacher told John to "seek after faith" in order to be saved. And suppose John follows the preacher's advice and tries hard to stop sinning, he prays, sings hymns, tries to be convicted by preaching, seeks to be around church members. But remember, he's doing all these things "in order to be saved".

In other words, the preacher has lead John to believe salvation by works. Every work John does of "seeking salvation" is actually an attempt to make himself better than other men (as if just being better than other corrupt people is enough to make the perfect God of the Bible pleased with you !).

In summary
1) regarding unbelievers -- all their "seeking", all attempts to "stop sinning", to "prayer" and all feelings of "remorse" -- all these things are sin (Heb 11:6, Rom 14:23).

2) in fact, any attempt by an unbeliever to "seek salvation" will only increase the damnation of an unbeliever. For example, any attempt by an unbeliever to "humble" himself and "seek faith" shows that this unbeliever thinks Christ's work was incomplete and insufficient. By thinking that humility is a requirement for salvation, the unbeliever is showing he thinks something is required of him ON TOP of the work of Christ. He might as well say "Christ died in vain".

3) popular preachers who tell unbelievers to "become humble" and "seek faith", are saying that Christ didn't do enough, and men need to add to the work of Christ in order to be saved.

"whatever is not of faith is sin." (Rom 14:23)

"without faith it is impossible to please God" (Heb 11:6)

EXTRA -- Discussion with Tad (a Calvinist from GA).