Q:

Is it possible to save the Crime Net public server filter settings?

Each time you enter Crime Net, the public server filters are always returned back to their default values - showing games of any difficulty, contract, etc.

Is it possible to save the public server filters settings rather than having to set them individually each time you enter Crime Net?

A:

I'm afraid it's not possible so far: I've been looking after the same feature, and all I could find were complaining steamcommunity threads, just like this one.

Please make the Crime.net filters persistent
  It gets annoying to have to set six different parameters every time I go to the Crime.net
  looking for a specific job. I'm sure many others would also appreciate this.

Also, note that, as one of the answers states, the search filters only reset if you close the game, or if you leave a lobby you've just hosted.

