In a follow up comment in here I explained two ways in which BIP110 transactions would be rejected by the bitcoin network.
"1. There are two ways I identified in which BIP110 transactions will be incompatible with Bitcoin. One is due to coins on BIP110 having a shared history with BIP110-mined coins which would be unrecognized on Bitcoin. Another is when transactions end up being mined on BIP110 instead of Bitcoin. Even if a transaction would otherwise be valid on both chains, these are two scenarios where it that cross-chain compatibility would break."
In a follow up comment in here I explained two ways in which BIP110 transactions would be rejected by the bitcoin network.
"1. There are two ways I identified in which BIP110 transactions will be incompatible with Bitcoin. One is due to coins on BIP110 having a shared history with BIP110-mined coins which would be unrecognized on Bitcoin. Another is when transactions end up being mined on BIP110 instead of Bitcoin. Even if a transaction would otherwise be valid on both chains, these are two scenarios where it that cross-chain compatibility would break."