This comment from the hot takes thread and my later response did get me thinking about what everyone here considers the immutable design elements that inform a character; stuff that if removed, effectively makes the character no longer them. For example: Batman's cape and cowl. If you see a silhouette of Batman, they're all you really need and you know "that's Batman!"
In a movie, if the bat chest logo doesn't immediately pop out or is absent, he could still look like Batman. But if you change the cowl? The whole thing falls apart. He's just goth Space Ghost now. His pointed cape is used so very much in creating imagery and his overall design that a capeless Batman doesn't really look right, albeit not as strange as a Batman with a different cowl. So there are certainly degrees of immutability.
There are many examples, almost none of which are universal, but become major talking points. Green Arrow's beard, Superman's trunks, Superman's spit curl, Diana in heels (this one used to be really big, but not as much in recent years), Arthur's hook hand, etc.
Obviously this changes from each person's personal takes, but what are some of yours? What are the centerpieces of designs that bring a costume together and inform a character?
Pictures very much welcome!