Let's say I have broadcast two transactions. Both of them are spending same UTXOs and are still unconfirmed.
Miners are free to include any of transactions and there's nothing to stop them. They can include the one made later even if it's paying lower fee. They can ignore the one paying higher fee even if it has been made earlier. They can include any of the transactions regardless of whether the original one (the one made earlier) has been marked as RBF or not.

Although miners are free to include any of the transactions, they usually use the rules mentioned in BIP125 standard.
According to BIP125 standard, the original transaction can be replaced by a new one if it has been marked as RBF, the replacement transaction spends at least one of inputs of the original transaction and pays a higher transaction fee.

Again, miners are not forced to follow the rules mentioned in BIP125 standard. But they usually do so and that's why I said "If your transaction hasn't been marked as RBF, it's very unlikely that you succeed in replacing that with a new transaction spending same input(s)."
A miner can break the standard rules for any reason. For example, because it's their own transaction or because they have been paid by someone.