Well, the Klingons in Discovery look very different from the Klingons in TMP/TNG. So I guess we should use Gene's logic again and just assume that Discovery's Klingons are what they always looked like and TMP/TNG just lacked the budget to represent them correctly?
The Klingons in this version of Star Trek have a particular look, and the Klingons in the other versions of Star Trek had their own looks. To me, there's no need to get hung up on it.
Kor