Who saved people before ~33AD? In most cases people were required to save themselves by applying the law. For example if someone was ignorant to you and poked out your eye, you where to reply with the same reaction, therefore saving you from future confrontation.
Still though even in those days God decided to come down and save the people. With Moses for example, the 10 plagues, splitting the water, the manna in the dessert, etc. And many man other times and places, God finds his glory in coming down and knocking people straight. One instance that I thought was really cool, is as follows:
2 Chronicles 14:2 - 16:12
The exact date isn't important but at some point about 2000 years ago Christ died on a cross. Since that point Christians everywhere have put their faith in Him. I feel that many have put the wrong kind of faith in him, and/or expressed it poorly, including myself.
He claimed to be the Way, the Truth and the Life and that nobody could get to the Father except through faith in Him (John 14:6). Yes, Yes he did.
That's great for everybody since then, but how were people saved before that? To points out how few will be really saved read (1 Peter 3:18-20). Also again Jesus himself states how few (Luke 13:23-24). Yet still, depending if this message is to those that have already died, or those that are spiritually dead I do not know but it is written:
For this is the reason the gospel was preached even to those who are now dead, so that they might be judged according to human standards in regard to the body, but live according to God in regard to the spirit. (1 Peter 4:6)
So either the spirit of corpses can return to happiness, or the spirit of depressed one (which I favor) will return to happiness. For it is also said:
He is not the God of the dead, but of the living. You are badly mistaken!" (Mark 12:27)
There are many more years of history before that date than after. Was there a different savior for them? No the Same God has been here to save us.
Did they just believe in God but not in Jesus? This is that same thing. So no.
In very broad strokes, what does Christianity say on this matter (general doctrine) and more specifically, are there differing views on this held by major branches of Christianity? If so, what is a summary of the different doctrinal positions? Catholics put their faith in the Eucharist and the prayers of Mary, baptists put their faith that Jesus died for them regardless of repentance, Some put their faith on both, Mormons put their faith in what they do, and Jehovah Witnesses put their faith in saying a name. These are all avenues of faith, and it is not a point of right or wrong or which faith is correct. It is that faith must grow to produce the fruits.
But who humbly accepts the truth, and does not reject the spirit?
“You stiff-necked people! Your hearts and ears are still uncircumcised. You are just like your ancestors: You always resist the Holy Spirit! (Acts 7:51)
Who knows how fearful the truth is to rest on you! Who gets severely angry when they learn the offensive truths! Why do they get angry? Because pride is in their heart, and they separate themselves from Love, and they can't believe what has happened, so they call for death. In the ignorance, they call themselves to the grave. Humility however, it has been said:
He has shown you, O mortal, what is good. And what does the LORD require of you? To act justly and to love mercy and to walk humbly with your God. (Micah 6:8)
Whoever claims to live in him must live as Jesus did. (1 John 2:6)
Otherwise we trip on the stone of truth and fall into depression and anger, then after tear apart what God has put together.
Clearly I say to you that the Kingdom of Heaven stares you in the face! And hard it is to enter without humility and faith that you are forgiven, and also faith that God will fight for you against the lie.
For in days of old Mom and Dad argued, and the children cried out for it to end. And the only thing that can save us, is the Jesus, his teachings, his way, and our change within.
For if you gain no understanding of the spirit while you are alive, how will you be able to use the spirit to reconstitute your body?
For those who exalt themselves will be humbled, and those who humble themselves will be exalted. (Matthew 23:12)