Our grey water is going into our septic tank. Hasn't caused a problem so far, but we are using all the Ecover products for clothes washing, dish washing etc. These are biodegradable and septic tank friendly
On most washing products now, the packaging will say whether they are suitable for septic tanks, so it must be common enough practice.
Our neighbours recently got work done, and their grey water is going to a soakaway with soap trap.
Now that we are getting work done, we asked our builder and he said that we might as well leave well enough alone, i.e. if it 'aint broke.....