Pretty much all of that is about control. Both good, "Don't eat the pig, for it is unclean! (when really it'll just kill you with bacteria)", and bad, "We need more babehs! Homoseks is bad!", and indifferent/just weird, "Don't mix fabric! Or rotate crops! (Seriously, what is this about?)" You can't expect dumb peasants to know all the details, so if it's a cultural thing they grow up in it, and do the things that will keep them alive without knowing why. Same thing has been documented in Indian and Pacific islanders and peasants, the women in the villages will avoid certain foods that lead to higher miscarriages without knowing "Why", just "it has always been done", or "it is magic!", or some sort of explanation that's not really an explanation, just something to fill in the gaps that human brains NEED to have filled and let them get on with their day/lives, without expending too much energy that they need to survive to find out exactly what's going on.
And the infallibility is to prevent pretty dumb bronze-age peasants from asking "WHY is the pig unclean?" and dying of... cholera, or whatever it is that pigs have. Whatever, you get the idea.
The priest bit is probably more control, pretty obvious that, though HOW it could be control beyond "HAHA I GOT POWER" I don't know. Maybe it just IS about the power, though why people go along with it in the beginning I don't know.
Not so necessary now, average level of education has gone up, pigs and such have become less "THIS WILL KILL YOU", population is huge so no need for babehs so much, and it's kind of like an old man on the end of the street yelling "I'm RELEVANT, damn it! Listen to me!"