While regular brands exclusively work by imprinting themselves onto the culture (see Advertising may work by cultural imprinting), cultural brands establish a bidirectional relationship with culture: they are simultaneously building and influenced by the culture. They do this by identifying a target/muse audience and giving them the tools to remix the brand however they see fit.
A good example of this is the Brat phenomenon kicked off by Charli XCX, where she gave fans access to a Figma board that they could use to generate their own “brat” memes. Brat became, for all intents and purposes, a cultural brand by giving its audience a platform for expressing themselves and facilitating rather than leading discussion.
An open question is—how do brands do this while still maintaining coherence and consistency? Or do they even need to worry about this?