Pet hair is amazingly tenacious. I think you might be best off just biting the bullet and telling people you can only do quilts that come from pet-free homes. That fur is GOING to end up in your house if you bring it in, there's just no two ways about it. Kindness and charity are very good things, but not at the expense of your own health.
My sewing room is a pet-free zone, and yet there's fur all over stuff in there. It comes in on my clothes, and it just drifts in through the air. I lint-roll constantly, but there's always more fur. I made a quilt for my aunt (who is very allergic to cats and currently going through chemo) and I washed it FOUR times in a row and then put it into a vacuum-sealed plastic bag straight out of the dryer...it still had some fur on it by the time I gave it to her! Fortunately it was very CLEAN fur by that point and didn't trigger her allergy, but still...couldn't believe I was still finding fuzz!