I don't claim to know what the reconciliation movement or whatever it is called teaches other than the basic points I've deduced from the posts here.
However, it sounds somewhat similar to the idea of recapitulation. This is the teaching that all of creation is being renewed through Jesus Christ.
All things are being drawn into Christ and through him are being made new.
The thing that people take issue with here, which is not present in the idea of recapitulation, is the universal nature of salvation and the non-existence of hell (I'm using the term to refer to ghenna, the place of eternal punishment, not to hades the place where the dead wait).
The key issue in recapitulation... and indeed in all of Christianity is the idea of 'in Christ'. Renewal takes place in Christ.
Many people struggle with the basic question "if Jesus died for all sins of all time, why aren't all sins forgiven then?"
The two answers to this question are generally "you must accept Jesus into you heart for his sacrifice to take effect" or "you must have been elected by God for the sacrifice of Jesus to have an effect for you."
There are positive points for both of those answers, but also problems for both.
I suggest that the real answer is found in the idea "in Christ". It is hard for the modern mind to really get a hold of what I'm talking about because it is somewhat mystical (or you might say spiritual.. the problem is that too many people think spiritual means figurative or metaphorical and both are wrong).
Both of those answers above, "give your heart to Jesus" or "be elected" ultimately when broken down are about believing, or claiming to believe the correct set of doctrines/ideas, and/or living by the right set of rules.
You can say (as undoubtedly most would) that election has nothing to do with either of those things... but the reality is it does. Simply ask the question, how do you know if you are elected or not? the answer is what do you believe and how do you live.
It is certainly not wrong to require correct beliefs and obedience. Heaven forbid I should ever believe or teach others to believe such a thing. However, there is just something off, something thats not quite right in the idea that you obtain salvation by claiming the right set of doctrines or following the right set of rules.
Those things are necessary, but ultimately they are not the point in and of themselves.
The real issue is being united to Jesus Christ, being in communion with Jesus Christ, his life being your life, his heart being your heart, etc.
This is the real point of the incarnation. So often it is taught that Jesus became a human so that he could pay the price that humanity owed. Thats fine, but really its secondary. He became a human so that we could be united to him and in so doing, become like him.
The ministry of Christ is like a second creation and in fact there are symbolic paralells between his ministry and the creation. Creation begins with the Holy Spirit hovering over the waters... Jesus ministry begins with the Holy Spirit descending over the waters of his baptism, like a dove with fluttering wings.
The creation story ends with Adam being put into a deep sleep and Eve being made from Adam's side. It was important that she was flesh and his flesh in order that they could be true companions and that they could become one.
Jesus' earthly ministry ends with him on the cross, being stabbed in the side and blood and water flowing out of his side. Blood and water are communion and baptism.
Like Eve, we the Church, the bride of Christ have been taken from his side that we might be flesh of his flesh and be united to him.
All of the things that Christ has made available, salvation, redemption, renewal, atonement... it is all found only in him.
You can not have communion with Christ if you don't believe the truth, and you can't have that communion if you refuse to obey... but in and of themselves, believing a set of doctrines and following a set of rules are useless without the communion of being in Christ.
This is the real reason, also, why some people will not be saved. Only those who are in Christ have life eternal. Only they have been reconciled to God.
I believe, without a doubt, that even if those who experience hell and torment were offered the chance (which maybe they will be I don't claim to know) they would still refuse that kind of relationship with Jesus. The reason being they hate God more than anything and for them submitting to that relationship would be more intolerable than the hell they are in.
Everything that is being brought into Christ is purified and refined by fire. Even the creation itself will be consumed in fire to emerge as a new heaven and a new earth. I have no doubt that there will be many people who will utterly refuse to ever submit to that.
They will prefer the fire of torment to the fire of purification.