The transport biofilters are described (in the TNG Technical Manual) as being able to deal with known dangerous bacteriological and viral forms. The Phage appears to be something different, a disease which directly infects the DNA (at birth) and then ravages it from the inside out.
Biofilter. Normally used only in transport to the ship, this image processing device scans the incoming matter stream and looks for patterns corresponding to known dangerous bacteriological and viral forms. Upon detection of such patterns, the biofilter excises these particles from the incoming matter stream.
It seems likely that a condition that is so closely related to the DNA of the Vidiians that the transporter simply reads as part of their normal physiology.