I would think that these particular questions are not troublesome. I don’t know of a parish that has told people to leave the building because their hair was not the right length. So this could not be fundamental to the faith. The second example is more complicated, depending on what it means. It doesn’t refer to what happens at mass, because the congregation doesn’t speak up during the ceremony. I’m not sure what it means myself.
Perhaps though you are asking about much larger issues? This whole matter has been a great bone of contention. There are those liberal in religion who maintain for example that what the Gospels say about Christ is mainly an invention of the early Church, based in large part on the religious ideas of the times. Personally, I have dealt any possible confusion in this matter by focusing on orthodox Catholic Biblical commentaries in my reading, such as the Navarre commentary series on the New Testament.
The parable of the shepherd and the sheep in John 10 gives me some consolation in this matter. Chirst said that his followers hear his, the shepherd’s, voice and they do not hear the voice of someone else or follow them. The faithful can see when some teacher is serving to undermine their faith and lead them away from Jesus, as he says himself in this parable, and so they can be protected.