Ahh, yeah, of course. If you taint it. But if you don't taint and don't opt in, then it can be stolen.
So yes, if you are on the Core chain, you can protect against replay, but only if you opt in. If you don't opt in, then they can be stolen on the other chain.
I had mentioned specifically post-fork coinbase output taint; if it's tainted, there's no way to replay, that's in fact one of the proposed replay protection mechanisms (unfortunately it's of the "opt-in" variety).