Why is there whitish gunk in my fridge water even after changing the filter
Found this on Appliance 411:

I have heard a number of complaints recently that the chemicals (specifically chloramine - a mixture of chlorine and ammonia) used in some water treatment facilities are causing the material the molded plastic refrigerator water reservoirs are made from to break down resulting in white or whitish particles appearing as flakes, flecks or specs in the dispensed chilled water. In that case the water filter is not usually the cause, instead replacing of the chilled water reservoir itself may be necessary.
Most manufacturers originally used a molded plastic water reservoir which is what seems to be effected and breaking down. Many fridge manufacturers are now selling a coil of plastic tubing (like that used in the rest of the refrigerator's water system) in place of a molded plastic reservoir.