Indeed, because the transaction signature and hash will be the same on both chains.
Someone could then copy the signature + hash to spend the same amount on the other chain.
Lets say you have Bitcoin X and Bitcoin Y. Bitcoin Y just forked so all the UTXO's on Bitcoin X are also present on Bitcoin Y. ( Bitcoin Y has no replay protection).
You try to send 1 Bitcoin X to your exchange adress, that bitcoin X generates a valid hash + signature, ( for the transaction to confirm.).
Now that hash + signature will also be valid on the Bitcoin Y chain, meaning that anyone could copy it, and sent/transact your Bitcoin Y.
Note that the amount must be exactly the same ( otherwise the hash/signature would be invalid again.)
There's some interesting answers on how to prevent them here - > https://bitcoin.stackexchange.com/questions/52210/what-is-the-best-way-to-prevent-replay-attacks-in-the-event-of-a-bitcoin-hard-fo/52260#52260
Thanks. The best description I've seen so far. Very explicitly and short