Since when are Bene Gesserit secrets public knowledge?

I found it very odd that the writers had people openly talking about Bene Gesserit secrets right there in public in both films, when in fact, the Bene Gesserits were a highly secretive organization. They guarded their secrets on purpose, due to wanting an air of mystique about their order, as well as hiding some aspects of their abilities that would scare the living shit out of the public if it was widely known.

A fine example of the errors in the film would include Chani yelling about the Bene Gesserits starting the prophecy for all the Fremen in the tribe to hear, when in fact, the prophecy had been started so long ago that most people on the planet had forgotten its origins. Her yelling about how Lady Jessica surviving the Water of Life Ceremony being a lame trick, (and Paul confirming it) also flies in the face of outright blabbing of the Order's secrets in public, which goes against how the Fremen viewed the ways of their priestesses.

Another error would be making Lady Jessica's Water of Life ceremony so informal and right out there in the open. No Bene Gesserit would ever hold such an important ceremony like that out in the desert, dressed in an stillsuit, for all to see. It was always a semi-private ceremony done far underground (at least on Arakkis), with trusted friends and maybe even family nearby, with the regular Fremen waiting in a more public area for news of whether they had a new Reverend Mother, or they had to old a funeral. (Not all Bene Gesserits, even with extensive training, survived the Water of Life Ceremony).

Showing that lame flashback of Lady Jessica as a baby being revealed to a [currently fat] Baron Harkonnen was a terrible idea too. The Bene Gesserits guarded their secret breeding program very closely. In the original lore, they never told the Baron whether he had fathered a child or not (which was common practice, and it's interesting that they kept it up with the girl who bred with Feyd Ruatha earlier), and at the time of Lady Jessica's conception, the Baron wasn't a floating fat man yet. I'm not sure if the flashback was meant to be symbolic, or if it actually happened according to Villeneuv's interpretation.