This cannot happen, if the mempool node is not full RBF enabled. Any transaction that does not contain the RBF flag will not be accepted. However, if it is full RBF enabled, the old transaction will be removed, and what you say can only happen in two different nodes, so that when you broadcast your transaction to a node Your old transaction in a different mempool will have been confirmed, as the miner has mined the block and included your transaction, and here the new transaction will be invalid.
But if you mean Child-Pays-For-Parent transaction, it is different from RBF.
You might have quoted me out of context I didn’t say both transaction can be in the same node’s mempool but rather both transactions have the tendency of getting included in any mined block since both transactions actually existed but in different nodes mempool so it is a matter of which of the transactions gets confirmed first and the other becomes invalid. The first two lines of the post you quoted was where I said so.
To be clear, if first transaction is in Node A mempool, (this node doesn’t supports full RBF) and the second transaction is in Node B mempool (this node supports full RBF). Then the first transaction can still get confirmed if miner owning node A mines a block first before miner owning node B and it included first transaction in its mempool, this means the second transaction is invalid even though it has the higher fee