I was out last weekend with STW not working (paddle wheel fouled as is often the case), but with SOG/COG present and displayed on FI-504; the FI-501 was not showing any difference between apparent and true wind.
The speed wheel on the transducer if installed, must be functional. The Smart Sensor with a fouled speed wheel will output 0 kts in the PGN for Speed throught the water, hence the same reading for true and apparent. The speed wheel will have to be kept operational as there is no selection for the speed source on the FI501.
You would have to disconnect the DST800 and then the FI501 will use the GPS data (SOG). Disconnecting the DST800 eliminates the PGN for STW which is the problem because it is sending data showing the STW as 0 kts. You can test this by simply disconnecting the DST800 temporarily and the true readout will use SOG for speed.
However, I suggest a firmware upgrade for the FI-50's because using STW is inherently inaccurate in a current. A setting that would allow a prioritization between COG/SOG and HDG/STW would enable much more accurate information. Using STW/HDG when in a 3kt current is pretty useless and I can't disconnect the DST800 without losing my depth data.