The UTXO set represents all spendable pieces of Bitcoin. A fullnode must have all UTXOs in order to be able to validate transactions. If some nodes were to discard some UTXOs and these UTXOs later get spent in a transaction, the network would fork as some nodes follow the blockchain in which the coins get spent and others would start forming an alternative chaintip.

There have been several cases of "blockchain graffiti" in which messages were left in pubkey hashes, and counterparty/Stamps deliberately used 1-of-3 bare multisig outputs to store data in two of the public keys (leaving the UTXO spendable per the third key). Recently, Citrea announced that they would store some data in pubkey hashes to embed non-malleable data in transactions with timely confirmation. A part of the motivation for dropping the OP_RETURN limit is that some consider it harm reduction to allow OP_RETURN payloads of 100 bytes instead of Citrea forging ahead with writing permanently to the UTXO set.

Any non-zero unspent transaction output that is not provably unspendable.

An output script starting with OP_RETURN is provably unspendable, so it can be pruned.

But an output with a fake public key or fake script hash (such as produced by STAMPS) is unspendable, but that's not always obvious. Thus these outputs must be retained in the UTXO set. These are the most harmful ones.