According to How & Wells, many of Herodotus’ claims in these sections of Egyptian customs must be taken with a grain of salt. For instance, his generalizations are simply that, generalizations and not representative of all Egyptians (especially the upper class).
Certain customs, however, seemed to ring a bell for me, especially those that relate to the philosopher/mathematician Pythagoras (from How & Wells, vol. I, p. 183): “Herodotus is right that the priests were forbidden to eat fish. This food might not be offered in sacrifice; hence the Pythagorean refusal to eat fish may have come from Egypt…H. is right that the priests did not eat beans” and so neither did Pythagoras nor his followers.
Indeed, the Pythagorean cult kept its silence about many rituals, like the Egyptian priests did and like modern college fraternities/sororities do. However, this religiosity coexisted with brilliant insights into mathematics and music. Were the Egyptian priests masters of mathematics? Are the pyramids proof of this or not?