The miners in the two chains gain from listening to what is going on in the other chain, and could just copy transactions and take the commission.
Have no miner attempted to grab some fees? Or maybe the price of ETC is so low that it would be unprofitable?
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Addendum:
It is addressed in EIP #155 [1], where they changed the signing of transactions and put some sort of chain identity to be included in the transaction signatures.
Which brings the question: Is there something changed in transaction signatures in the segwit2x hard fork? Is there already some chain identity in it?
In btc1 there is not any replay protection right now, as the timeline didn't allow for development of this. It is an important feature request though, maybe follow along here:
