There are open world rare mobs in BFA zones which have a chance to drop loot on a daily basis. Whether or not you get the specific loot piece when killing a rare, the addon considers the mob defeated and thus no longer tracks and shows you that you do not have the specific item which drops from it

Can you screenshot a specific example? This is definitely not how the addon actually functions for all situations.
If a specific Thing is only available from a specific rare, it won't be hidden just because you are saved for the day.
If it's available from other sources as well as the rare, it might be listed in a way that it no longer shows in the minilist once the rare has been saved for the day, but only on a character who is saved to the rare.

So.... while working on making an example of my issue above it has come to my attention that the items from the rare's are marked as uncollected if the said rare was not defeated on the current character, and in the second screenshot, there's an instance of the addon showing the same item as both collected and uncollected.

After a relog the rare and the item disappeared from the minilist, so I opened up the debug mode where the specific item was marked as collected.

Looks like that's supposed to show a circle checkmark, you don't have the appearance from that source.

Ok the one weird part about this is the item showing uncollected and then collected in next screenshot... You're saying this changed without you having actually looted this item, correct?

Other than that, it looks like you have Account-Wide Quests tracked, as well as Achievements (maybe not account-wide??). So these BFA rares are one-time quests technically, hence they are collectible themselves as a Quest. Each is also required for an Achievement, hence the sub-collectible Criteria for each Rare, (but the achievement in its entirety seems to not actually be collected, thus the Criteria continue to show under each rare which is not yet killed on the current char). And finally some have random other collectibles like Appearances that show up, so up to 3/3 for a Rare.

I assume you are using the +Sources option for Appearance collection? Seems a bit odd that the appearance was uncollected and then become collected even though your other add-ons say it isn't known from that item...

These are my settings which that I'm using on every character.

The second screenshot above is definitely the weirdest one with the same item being repeated and having X and a checkmark at the same time, and weirder still is that whatever the issue was practically went away.

I made a cloth trial character and checked the Bfa zones and it currently just lists the rares as undefeated with the items collected, and did the same with a plate class.

Refreshing the collection hadn't loaded the items as obtained when I was trying to see what was wrong, but perhaps going into the debug mode did the trick?

The whole thing is weird, but whatever it is I'm just happy it's working okay now.