How do you deal with tuning "non-singers"

There are "singers" that do not fall into the category "pitched notes" or... "approximating a scale known to mankind". I didn't have that for a while but if there is such a singer i just let them do their thing and do nothing - on the two occasions where it happened nobody asked me to "fix" it, as it is what it is and if it would need fixing, than that fix would include to swap the singer.
On another band a person with a very strong lisp was the singer. Intentionally. No need to fix that either. There is music that is off grid, so to say, in many ways.