On average, Americans receive a radiation dose of about 0.62 rem (620 millirem) each year. Half of this dose comes from natural background radiation. Most of this background exposure comes from radon in the air, with smaller amounts from cosmic rays and the Earth itself.
So, cosmic rays contribute hardly (about 4%) any to the radiation we receive every day.
I’m no expert here, clearly, so I’m not sure how to compare these units of radiation with the ones being provided for the Fukushima water release; those numbers are provided in becquerel from the sources I found.