No.
While I think it's possible for the Grace of God to work in different church communities, there cannot be different Communions of Churches that are equally the same, because that would mean that God - who if infinitely good, and infinitely love - views contradiction and lies as equivalent to Truth. Did Christ ever lie?
The Roman Catholic Church firmly believes in the dogma of the Immaculate Conception - that is, humans inherit the guilt from the sin of Adam and Eve, and the Virgin Mary was exempt of this inheritance through God's grace.
The Orthodox Church views this as heretical, some even going so far as to say it's blasphemous, because it says that someone as holy as the Virgin Mary couldn't have been that sinless on her own free will. They deny this idea of the inheritance of the guilt of Original Sin, so thus, the Immaculate Conception cannot be True.
Therefore, it must be the case that one of these Churches is right, and one of them is wrong. They cannot simultaneously be right, or say that these ideas are "the same" but "expressed in different ways." They are contradictory ideas; one is blasphemous, one is divinely revealed truth.
If there weren't contradictions, there wouldn't be the schisms we see today.
This even gets into moral issues as well. The Anglican Church believes it's morally acceptable to ordain women. The Orthodox Church and the Roman Catholic Church say otherwise. They both can't be morally right, and this is merely an issue of Church ecclesiology, not even controversial topics of Abortion, LGBTQ, Contraception, etc.
Again, they both can't be right.
Also, all the Apostolic Claimant Churches (Anglican, Orthodox, Roman Catholic, etc.) hold to a principle of Apostolic Succession that is different than how you describe it. It isn't just merely that you are descended from a particular literal Apostle; rather, your Church contains the fullness of the Church, of the Apostles, of the Saints, in each Bishop which can all be traced back to the Apostles. Each Bishop is a successor of the Apostles; Saint Ignatius of Antioch points this out with "Where the Bishop is, there is the Church." In order to be a successor of the Apostles, you have to teach exactly what the Apostles taught.
This isn't a new idea you are espousing, it's an idea of "branch theory" that both Orthodox and Roman Catholics (at least historically) have explicitly condemned as heretical. As Saint Paul says, "One Faith, One Lord, One Baptism."
Plus, it's not like the Apostles were isolated. They were in contact with each other and kept tabs on things; Saint Clement had to deal with the problems in Corinth. I mean, yeah, Saint Thomas in India probably didn't keep tabs on Saint Paul in Greece, but it's not like they were isolated figures who didn't talk with each other and who expressed dogmatic Truth differently.
Regarding your example, the Immaculate Conception, I have a couple of points to make. Whether you agree with the reasoning or not is not the point. It is the logic of the Church. I understand that people don't see this, but this is what the Church sees:
"And the angel came in unto her, and said, hail, full of grace, the Lord is with thee: blessed art thou among women." - Luke 1:28
It is the term "full of grace" that is emphasized by the Church when dealing with Mary's Immaculate Conception. The title "full of grace" comes from the Greek word
kecharitomene, which describes a "perfection" and "abundance" of grace. In other words, Mary was proclaimed by the angel to be with a perfection of grace, which was a very powerful statement. How can Mary be completely and perfectly with God's grace, yet still have sin left in her? Christians eventually came to recognize that it was extremely possible for Mary to be without sin, especially if she was completely filled with God's grace. Luke 1:28 happens to be the only place in the Bible where anyone is addressed with the important title of "full of grace."
"the Holy Ghost shall come upon you, and the power of the Highest shall overshadow you: therefore also that holy thing which shall be born of you shall be called the Son of God." - Luke 1:35
Luke 1:35 shows Mary as the Ark of the New Covenant. According to the Old Testament, the Ark of the Covenant was the pure and holy vessel that held the Ten Commandments (the Old Covenant). The Ark was so holy in fact, that if anyone where to touch it they could actually fall down and die! It was housed in the Holy of Holies, which was a perfectly clean place where the Jewish high priests could enter only once a year according to their law (See Lev. 16:2-4). So how are Mary and the Ark related? The same language that describes God's "dwelling" place for the Old Ark is used again for Mary's
overshadowing by the Holy Spirit. Put another way, the Old Ark held God's Ten Commandments and could not be touched by human hands because of its holiness. Mary, the New Ark, holds the New Covenant in her womb, which is Jesus Christ. How much holier is Christ than the Ten Commandments? It only makes sense that for Mary to hold God in her womb, she too would be completely pure and without any sin.
"I will put enmity between you and the woman, between your seed (offspring) and hers; He (she) will crush your head while you strike at his (her) heel." - Genesis 3:15
What does the book of Genesis have to do with Mary's Immaculate Conception? Genesis 3:15 is the first passage in the Bible that refers to Jesus defeating Satan on the cross. It is also the first verse that shows us how Mary would become the New Eve. The seed of the woman, who would crush the serpent's head, is Jesus. The woman at enmity, or hostility with the serpent, is Mary. It was God who put this hostility between Mary and Satan (the serpent), and it is believed to be in the same
likeness as Christ's hostility for the seed of the serpent. What exactly does all this mean? For Mary to be like Christ in His hostility for Satan forever, it is very possible to say that this passage implies Mary's lack of sin. What better way is there to be in total hostility with Satan than to be in God's constant grace? As the New Eve, Mary undid the "no" of the Old Testament Eve by saying, "yes" to carry Jesus.
Regarding the contradictions and schisms, those are man-made, not God-made.
