Assets can already have mutable data (attributes), but it's only supported on contract level, not yet within the NFT Creator (right now all attributes are auto-created as immutable).
Authorized accounts can change mutable data at any time.
If a certain attribute is already defined in a template's data, mutable data still won’t change it.
You can update the assets mutable data regardless of whether it uses a template or not. You just can't overwrite attributes that are already set by the template (precedence: template data > immutable asset data > mutable asset data).