I interpret this question to be a roundabout way of asking whether Ordinals may impact privacy on the Bitcoin network.
It is best practice that Bitcoin transactions shuffle the order of inputs and outputs. When order must be preset among multiple collaborators, it is preferred to use a pseudorandom deterministic order that looks random to uninvolved parties.
Since subscribers to Ordinal Theory have additional concerns regarding the order of transaction inputs and outputs, rare Ordinals or Ordinals imbued with Inscriptions present a fingerprint that informs chain surveillants’ attempts at identifying change outputs and clustering of wallet activity.
Additionally, Ordinal Theory reinforces the notion that satoshis can be uniquely traced and UTXOs are non-fungible. It’s reasonable to expect that the resulting behavior will impact the privacy of wallets of Ordinal Theory subscribers and—if Ordinal Theory should gain sufficient support—could transitively harm privacy on the bitcoin network more broadly.