What you are describing is not possible with transactional replication from a publisher to a subscriber(s).
Transactional replication replays the COMMANDS run on the publisher on the subscribers, in the order they occur. It does not transfer the "data" changed and it is not possible to skip commands from replaying.
When you run a command on the publisher like:
UPDATE table SET col1=xxxx
Transactional replication stores that COMMAND and runs the same command on the subscriber. If the command errors, it stops and will not continue with other commands until that problem is fixed or the command is manually deleted from the distributor commands table.
Unless what you are really using is "merge" or "bidirectional" replication. In which case, you can have "conflicts" in changes, and those are automatically handled and logged. See: https://learn.microsoft.com/en-us/sql/relational-databases/replication/transactional/peer-to-peer-conflict-detection-in-peer-to-peer-replication?view=sql-server-ver15