There is a S4 Enterprise arc which was clearly intended to explain the smooth headed Klingons (it’s a disease brought on by attempted genetic engineering, basically). If one wishes to find a visual literalist explanation beyond that, it would simply be that there are lots of Klingons out there and some of them look very different.

The other approach would be to accept that aesthetics change with budget and technology, and just shrug it off. I’ve grown increasingly supportive of that position as new material has come out, but it’s hardly a new take: Roddenberry himself, asked about the Klingons in TMP, said that they were always supposed to look like that, but the show never had the budget to make it happen.