Radioactive particles can only be filtered based on the fact they are particles rather than that they are radioactive.

The issue then becomes one of filter effectiveness against whatever the particle size is. (I wouldn't know particle sizes for such an accident)

The concern for the filter becoming radioactive is correct though the filter could only become a hazard to handling if it were filtering particles giving off gamma. Alpha and beta radiation wouldn't escape the filter body though the filter should be disposed of as radioactive waste when done.

An alternative method to create safe water would be to distill it. All particles would be left behind in the boiler.

Just be sure the revenooers know what you're boiling :-)