Adding -p just preserves the modification times, the copy will still happen.
make should only be running the command if ${LIB} is older than ${ACTIVE_CONFIG_LIB} - so that should suppress the code when not needed.
So something else funny must be going on, possibly another dependency line somewhere.
What you might need is something that only updates the config file if it has actually changed - that needs to be done before the makefile above is run.
Assigning to CP on the make command line and/or the environment should suppress the assignment in the makefle itself.