I am the kind of person who enjoys "big weird" scifi like Stanisław Lem. Stories about trying to relate to and find common ground with something so alien that the prospect of even understanding is basically hopeless. Star Trek usually doesn't do stories that, which makes sense as it often uses alien races as allegories or stand-ins for real-world human relations.
That said- I thought those early Klingons were super weird and scary because they were just so alien. It really made sense thinking about how it took a century before they could get to the events of Star Trek VI, and it made the Khittomer accords feel like so much more of an accomplishment. Like- you made a treaty with WHAT?
And just aesthetically their ships and armor looked like something out of HP Lovecraft or HR Geiger:
This is not to say I dislike how Klingons were portrayed previously, kinda like Mongols in TOS or Vikings in DS9, just that they never felt scary to me. They never felt like warriors. I was never afraid for the gallant crew of the Enterprise D (a science and exploration vessel) going into battle against Klingons. But I really enjoyed the alien-ness Disco tried to go with. Anyone else with me?
EDIT: PEOPLE I SAID WHO'S WITH ME NOT WHO ISN'T CM'ON 
I don't consider them different. I saw TMP for the first time after having grown up on TOS ans TNG and thought "oh they switched to TNG makeup for the Kirk movies?"
The irritation for TNG looking different than TOS also silly and misplaced. It's 100 years later. That provides plenty of time in-universe for things to drift and evolve from one depiction to another. It's the same reason why I have zero qualms in terms of continuity with S3 and s4 of Discovery.
So why can't you do that here?
TMP isn't.
I should clarify that people at the time of tng airing complained about the look of the series in general with the touch screens and carpets and stuff.
Rod at the time of TMP did imply the Klingon ridges were a retcon but it was never confirmed, and it's unclear how we're supposed to interpret the augment virus now with SNW reverting to the TMP/TNG look.
Personally I'd love for Kor, Kang, or Koloth to make an appearance without ridges in SNW.