Water discharge from a nuclear plant IS NOT RADIOACTIVE.  Nuclear plants have two completely separate water systems, process water and cooling water.  Process water goes thru the reactor, gets heated by fission, makes the steam, steam turns the turbine to generate electricity, then the steam goes to a heat exchanger to be turned back into water to repeat the process.   Cooling water is pumped into that heat exchanger ONLY and is in a completely separate loop from process water.  What is discharged back into the water is cooling water, it never went anywhere near the nuclear reactor and isn't mixed with the process water that runs thru the reactor.