Well stated.
Earlier in this thread I related a personal story about going through the motions with a tour group in Thailand for a Buddhist ceremony.
I didn't participate partially because I'm not a Buddhist and partially because I do think it is insulting to go through the motions when you genuinely do not believe something.
To be surrounded by people who sincerely believe in the ritual, while I think it is crap, is an insult to those people even if I am supposedly trying to "learn" about their culture or religion.
I can learn about their culture/religion by watching them do it. No need to participate, no need to insult.
It is a religious ceremony so it will contain metaphor and prayers and silences and burning of this and holy water that etc... if it was rocket science then, yes, I can understand the need to participate in doing calculations and doing some experiments in firing off some rockets etc...
The other funny thing from earlier in this thread is that I linked to a wiki page about rituals and purification: https://en.wikipedia.org/wiki/Ritual_purification
Prior to this case, I think any reasonable person looking at that page would agree, yes, those are religious rituals including a description of indigenous smudge sticks etc....
No one would have said anything about the use of the term "religious" on that page at all - we would all take for granted that ritual purification ceremonies are, inherently, religious.
But no, as soon as the story in the OP crops up the story changes and it is not religious but cultural, yeah, that's the ticket, it's cultural.
It is all so disappointing and disingenuous.