I was taught wrong / wrongly...

Well, we can't hold back the tides of change. I would use wrongly precisely because it is an adverb. As Tes yeux pointed out, one might say: "I was taught wrong," but one would not say: "I was wrong taught." One would say: "I was wrongly taught."

I once heard a short piece of drama on BBC Radio called "On Dover Beach" by Tom Stoppard in which the actor Alan Howard voiced two parts: Matthew Arnold and a notional ruthless critic, doing a demolition job on Arnold's most famous poem (one of my favourites). The critic points out that the poem's central metaphor was a turkey: tides go in as well as out. Not only that, whatever it was that Sophocles heard long ago on the Aegean, it wasn't the tide, since that sea is not tidal. Arnold groans "That's not criticism; it's oceanography!"

I would replace the word "wrongly" with the word "incorrectly".