i see, the BCH address format has changed.
i kind of think that if i have privates keys on both BTC and BCH, then can replay protection stops me from mining the same transaction twice?
Replay attacks allowed attackers to reuse a transaction from the BTC network to be injected in the BCH network, and vice versa, without using the private keys. But as BCH network changed their transaction format (and are incompatible with BTC transactions), your unspent transactions are now safe.
As far as I can remember, I believe the following spec is required on the BCH network: https://github.com/bitcoincashorg/spec/blob/master/replay-protected-sighash.md (but I didn't check in details).