There are a bunch of grey and white appearances I do not want to learn (especially anything with “rotten” in the name) and I’ve been destroying those since the auto-learn upon vendoring was added. Now I find that destroying also auto-learns!
Is there any way I can get rid of such items without learning the appearance?
Unfortunately no, I do not believe there is a way to unlearn or not learn an item appearance. You can make a suggestion in game or in via the forums in the Transmog section.
There may be an addon that allows you to filter out mogs you never wish to see.
Edit:
I do not wish to not see the appearances, because they are not unique to the items with gross names.
I think I might have thought of a workaround, partly. If I let the items expire in mail, they would not be auto-learned, I hope?
But that wouldn’t work for Soulbound items. But if it’s Soulbound I think it’s already learned, right?
Or, use the addon that Jeysca linked you to 
Problem solved.
So the addon can hide individual items within a single appearance?
Like I just learned a Fur-Lined Armor by destroying it (this is how I found out). Once I get the Rigid Armor (identical look) I can hide the Fur-Lined Armor from appearing?
In theory yes. I have not used that addon, not any addon, to hide an appearance.
I can’t imagine the headache of trying to juggle my mail and claim or not claim certain rewards so I don’t learn an appearance.
The addon is worth a try. Otherwise put in a game suggestion though I honestly wouldn’t get my hopes to high on a quick, if any, update to the system.
That’s odd, I was having to equip these items to learn them, before doing a vendor sell all trash. I understand you may not like the look though, but I’ve never had one that was not purposely equipped to learn it. I don’t know of a way to unlearn them either.
It was changed not too terribly long ago. Now selling or deleting will learn the appearance.
Deleting is honestly nice, since some items have a 2hr refund window. If you can’t equip it (wrong armour type) it just sits in your inv for 2 hrs taking up space. Deleting is a nice middle ground. You may lose out on any (usually small) vendor price but at least it’s not clogging up in your inv for 2 hrs.
Probably, i know for the longest time players requested lesser restrictions on what can be transmogged and would likely hate to just have something auto vendered and not learned.
Ive hopefully leaned most of these, so probably won’t have any in these sets to test though.
I believe you can toss greys onto the AH without learning them.
Now this is a reason to have the function. I had no idea why they would add such a thing, but now I do. Thank you!
This sounds like a much better way than mailing to another character. Thank you!