The Church cannot contradict Scriptures - ever. Were that the case, Christ would have never founded His Church, His kingdom here on earth. Certainly He could have commanded, "Go forth and tell folks to read, so that by private interpretation, they may be saved", but He chose to command them to "Go forth and teach" - which is what they did and still do.
Ignorance of the Bible is indeed ignorance of Christ, but our knowledge and beliefs of its contents derives from the teaching authority that Christ bestowed on His Church to define and explain certain things that are hard to be understood and wrested by many to their own destruction as 2Peter 3:16 plainly states. Thats one of the great things God did for us so that we all know which direction to travel heavenward together - not left to drift aimlessly scattered here and there.
But the church contradicts the Bible all the time. There are no scriptures that gives Mary the status that the church does. Mary is NOT Co-redemtrix, nor was she immaculately concieved, you are NOT to pray to Mary, etc, etc, etc. None of those can be found in the Bible. They are traditions of the church, not scripture. And if they are not in scripture, they are WRONG.