Have you tried to close and re-open your Operation View after you applied filter on the layer?
I have tested and it worked for me. Also, don't forget to save your feature layers in the web map.
I have tried re opening the Operating View, to no avail.
I have found though, that when I close and re-open the web map, it does not save the Filter either.
There is also no option to save the layer in the web map. Does it matter that the layers are MapServer layers that I am not the owner of?
I am currently dealing with the exact same issue. Extents, pop-up configuration, filters, etc. that are set in the webmap are not adhered to in my Dashboard. Were you ever able to find a solution?