Source: WowAce

Potential taint issue? Or just some UI changes due to the new mount equipment button being added?

Update: Definitely not a taint issue, but rather the equipped item being reset somehow.

Confirmed. As described, the equipped mount item is set to nil somehow and this will last until an actual logout (not just reloadui):

MountJournal_GetDisplayedMountEquipmentItem is nil when it should give a table value for MountJournal.currentItem

This is despite C_MountJournal.IsMountEquipmentUnlocked() returning true...

This doesn't seem to be caused by Rarity per se, as the Mount Journal is used in read-only mode to detect the collected mounts. Looks like using the MountJournal in any way can cause it to glitch and display this odd behaviour.

Also, I found lots of players describing a similar issue: https://us.forums.blizzard.com/en/wow/t/mount-equipment-gone/207624/51
It appears unlikely that they all would be users of Rarity, so in all likelihood it's a not-so-well-tested Blizzard feature and not a bug caused by the addon itself.

Therefore I'm submitting a bug report to Blizzard's QA team and hope they'll have it fixed before too long.