All people are equal and all deserve to be called upon to believe in Allah and His messenger. None is to be preferred on account of his high position. None is to be ignored on account of his humbleness. That Allah has chosen to give this very important principle in the way He has, making use of the incident I had just described in order to drive the point home is His own prerogative. We read this surah in the same way as we read other parts of the Qur'an.
Every portion is highly relevant and highly important.
We cannot ignore any part of it for any consideration whatsoever. The old man who told you not to read this surah often might have spoken out of love for the Prophet. We should remember, however, that no matter how dearly we love the Prophet, Allah loves him more. If we were to ignore this surah our attitude represents a protest against its inclusion in the Qur'an. This is not up to us to do.