I think nodes do this by default
Nope, if the transaction includes any INPUTs from a block post-fork, that transaction would be invalid on the Bitcoin blockchain side and those nodes would not relay the transaction.
However, long term support would require BUY-IN from the existing BitCoin developers because at some point they will lock-in a block CHECKPOINT outside your fork.
If the fork is trying to use the same port (8333) and it gained a following (i.e., a lot of nodes using it) then likely the Bitcoin-Qt/bitcoind client would treat these as harmful and possibly require an update to address this thread (e.g., have the client disconnect early after some threshold of invalid transactions is received).