Odd how God works.
The teacher then called all who wanted to be born-again up to the altar.
If this is error how far do we take it? Certainly many relaized on their own that they would never, outside of grace, understood their need. Its also true that many would argue that they must respond. Well dont we need to respond? Isnt the old time pentecostal 'coming forward' really a means to make a public confession of faith? Which is required yes?
When folks are taught and believe in the Trinty, the vigin birth, the diety of Christ and the physical reality of his death and resurrection are they in danger because they speak ,with tears, of the day they 'accepted the Lord' rather than when He accepeted me?
Hitch,
Lots could be said about what you wrote/asked. But I'll do my best to make my responses brief and to the point.

1. Asking if someone wants to be born-again is a serious error in doctrine for the new birth, aka: regeneration, born again, born from above, made alive, etc., is outside of both a person's ability and experience. Regeneration is a supernatural, secret and silent work of the Holy Spirit, which is clearly taught by the Lord Christ Himself (Jh 3:3ff). Additionally, this reveals that the person asking the question believes that regeneration follows faith. In short, IF you believe... you will be born again. Billy Graham holds to this heresy and even wrote a book with the title,
How to be Born Again. The bottom line is that those who hold the view that the new birth follows and/or is the result of faith, of necessity deny that fallen man is totally depraved; that is sinners are totally unwilling (no desire) and unable (powerless) to believe on Christ UNLESS the Spirit regenerates them first.
2. One can embrace and articulate all the doctrines of Scripture perfectly (hypothetically of course) and still be liable to judgment. The horror of all this is that the majority of churches teach that one only need to give assent to the "essentials of the faith" and "ask Jesus into your heart" and you are saved. Historically, this damnable heresy is called
Sandemanianism, or more popularly known as "Easy Believism". True conviction is Spirit wrought and affects the entire man; mind, body and spirit (the heart). When true conviction comes, the result is far more than a simple admission that one is 'separated from God' or one is 'guilty of sin'. True conviction brings forth the realization that one is guilty before God because of who he IS, not just that things haven't always been done perfectly. One also realizes that they are under the wrath and just condemnation of God; God is their enemy and they His. True conviction also reveals the inexorable holiness of God and the dire need to be perfect before God in order to be reconciled to Him. And, that also leads to one's insatiable desire to have Christ as one's own; Lord, Saviour, Mediator and Righteousness. There is much more that I could add here, but these are the universal elements which all who have been brought by the Spirit to Christ (Jh 6:44).
3. Not to sound like a broken record, but
IF a person who embraces Pelagianism, semi-Pelagianism, or Arminianism in their
HEART as well as their head, then they cannot be saved, for those systems of theology deny the very grace of God needed to be saved by adding their own "free-will" (autonomy) to that grace.