What happens if the transaction is resubmitted (following an initial transaction with the RBF flag set) with identical inputs and outputs but with recomputed signatures, changing the transaction ID?
Almost all wallets calculate the k value deterministically, so a transaction with identical inputs and outputs will almost always have the same signature.
In the rare case that someone used transaction malleability to change the TXID, then nodes would reject this new transaction since it does not meet the criteria for the increased fee as per BIP125. The original transaction would remain in the mempool.