You bet it matters. It's a matter of honesty. Did Christ teach this, or did He teach something else? Now, I nor God can fault you for that which you cannot know - either because you are ignorant or stupid. Natural stupidity is not a sin, and you can't be faulted for something you do not know.
But as Christians, we believe there is real, objective truth that goes on whether we believe it or not. If the Resurrection is something I made up just because I thought it sounded nice - I believe it is true for me, but not for an atheist - then I believe complete nonsense.
Part of the Christian life is to come to know the truth as it really is. Christ is "the Truth". So we ought not to fear the truth, but seek it. And part of that includes the one question around which all dogma and doctrine are centered: which authority has the right to say it is founded by God Himself?
I would argue that Rome has that authority. It was founded by two Apostles: the head of the Apostles, Peter; and the most vocal of the Apostles, the first theologian of our faith, Paul. It broke up the fights and squabbling when the Eastern Churches couldn't agree to anything. And even the Oriental Orthodox have one church that is not Orthodox, but Catholic: the Maronite Church has always been loyal to Rome.
Still, I wouldn't blame the man who chose to become Orthodox instead. The two (three?) churches are remarkably similar, Rome, and Constantinople (and Alexandria, and Antioch, and Ethiopia, and Malankara, etc). And they, too, have valid apostolic succession.
It's all really a question of how the Apostles passed on their authority. It's fairly clear an episcopal nature was used, and only preserved in the Catholic and Orthodox Churches. Anyone who argues the Church Christ founded was congregational or like the Presbyterians ultimately has to face that none of the Churches that survived the persecution of Rome passed on their authority the way the Baptists, Presbyterians, Evangelicals, or non-denominational Christians pass it on. The "Bible alone", in that way, just doesn't suffice.
And where there is no legitimate authority, there is no Christ, either, who is our sole authority, working through the bishops and priests.