Are aquatic filter feeders effective at cleaning water to a safe level?
My answer from the top of my head is that they will not be very effective at cleaning the water. One reason is that if the substances and organisms are harmful to the filter feeder as well, they will avoid eating them or they will die from them or have their health reduced. In either case they will be filtering less.

Another reason is that if you use the tap and replenish the water with new contaminated water regularly, the filter feeders will probably not filter all water in the tank, and the outflow from the tap will still contain the contaminant. This is certainly the case if the tank is also the culture vessel for your filter feeders. In this case, the tank has come close to being a continuous culture. There are decades of science (including R* theory) which show that resource levels in such systems settle at a positive level (and you propose that the harmful micro-organisms are used as resource or at least eaten in proportion to the resource if the filter feeder cannot be selective). This positive level will then thus also be present in the effluent from the tank (your tap water).

An alternative is to grow the filter feeders in a dedicated tank, and than add them later in high concentrations to your drinking water. This would not be efficient because you need to feed your filter feeders with something.

Finally, the harmful substances may be absorbed by the filter feeders, but also be excreted, in which case the will end up in your drinking water anyway.

For getting rid of the harmful micro-organisms, it is probably more efficient to boil your water!