On my system, I filter it because we do a load of laundry about every three days.
The water usually never completely empties before more water comes in.
If you let the water sit around too long, it will start to smell like dirty socks.
My filtering is really simple though - gravity fed only, through some plants and a sand filter - no pumping or replacing filters.
If you just use water from a bathroom sink, straight to the toilet, no filtering is needed. That's a great little system.
In my case, I am working with about 30 gallons of water at a time, and have cut my water bill in half. (Believe it or not, water is my most expensive bill!
)
Every little bit helps though! Keep up the good work!