Do you happen to know how old your water heater is? If you don’t, go to Troubleshooting on waterheaterrescue.com, then to Lingo, then to Labels to find out how to determine that.
That said, it sounds for all the world as if your dip tube is disintegrating. There was a debacle some years back involving the formula for the plastic from which dip tubes are made, and just this kind of problem. In the aftermath, the company that makes them switched from a white plastic to blue to differentiate the old, problem dip tubes from the new.
Nonetheless, if you’ve got blue plastic bits in your aerators, they are likely from the dip tube. Go to Preventive maintenance from the waterheaterrescue.com home page and then select Knowhow from the pull-down menu for information on how to remove and inspect the dip tube.