Whether there is 'one' Catholic teaching or not, that is irrelevant. It is irrelevant because the multitude of people who comprise the Catholic Church are ~not~ all of one 'accord'. In other words, the Catholic leadership can claim they are all of one accord (they aren't) and that there is one 'official' Catholic teaching (which changes from time to time), but the people in the pew are not 'of the same accord'.
Whether there are 2 different 'thoughts' pervading the laymen of the RCC or there are 27,000,000 -they are ~not~ of one accord.
What I have never understood from this common objection is how it ~proves~ that the Catholic Church is the one true Church. Doesn't the Mormon Church teach the same thing? Are they ~necessarily~ the one true church as well?
Jean