Have checked the browser settings as well. They are normal and I have not changed anything there, still using standard tracking protection. I look at a ton of news and other web pages. Only the church web page is doing this.
The pop-up cookie notice shows only 23 bytes. That is extremely small. For example, I just logged back into the tech page to answer you and it shows 67 cookies totaling 3.1kb have been placed. The tech page and family search do not have the pop up, just the main church web page does.
Thus far, not accepting the cookie pop up notice has not changed my experience on the main church web page at all. I can still do all my ward clerk stuff just fine. So will keep not accepting it for now.
I remember when web pages in general required one to opt in to accept cookies but that was many years ago.
Am using Firefox 91.0 which came out on August 10. Perhaps that is the culprit, but as you say, there should be others reporting it then.