I still maintain that season 1 of Disco was a sly attempt to reboot all of trek into the alternate timeline Calvin-verse. I can't prove this though. To me, the aesthetics are all a closer match to what's going on in the recent Trek movies than anything done before all that. Season 2 saw the producers backpedal hard after fan backlash.
They steered them back towards normal looking after the first season for what it’s worth. They literally have a character comment, “Oh hey, you’re all growing beards again.”
The hair was one thing, but also their skin tone. Every previous Klingon has had a "human" skin tone. But in Discovery, each Klingon is entirely either a sort of dark blue, charcoal, or just straight up black.