They would accept a "transaction," sure, but it will just hang around harmlessly in their mempool unless it gets into a block. And it can only get into a "block" if a rogue miner decides to mine it according to the "old rules." The rest of the network will reject that block and mine new blocks without it, and "old nodes" will then follow whichever chain has the most work. So it won't cause a "meaningful" chain split unless miners are roughly evenly divided on which chain to mine. At most only one miner or so will still use the "old rules," and that's no big deal because the "majority" network will overpower that "minority" network with their greater hashrate, and even the "old nodes" know to follow whichever chain has the most work, as long as it doesn't violate any of their rules.

Which is why, before activating a soft fork, we usually have miners "signal" their agreement on the new rules via the bip8 method or bip9 method before we "go live" -- that way we know the vast majority are ready for the new rules, and a meaningful chain split is less likely to occur.

Remember: once your node accepts a block, that doesn't mean it's there forever in your copy of the blockchain. If a "longer" chain appears with "more work," and this longer chain lacks the block you accepted, your node will switch to the longer chain and discard the block it once accepted. Also, just because you "accepted" a transaction into your mempool doesn't mean you require a block to come out that has that transaction in it. Your node will chug along just fine even if that old-format transaction never gets mined, and even if a miner does add it to their block, your "old node" will discard that block if the rest of the network refuses to build upon it and makes a longer/more-work chain without it.