In order for the body to heal during a fast, it needs sufficient stores to live off of. Anorexics are already starving, and a lot of bulimics are also if they are always throwing up everything they eat. I'm not saying turn them away without any support, I'm just saying there is no way it would benefit them to fast when they are already damaging their organs by not eating or not retaining what they're eating. As for binge eaters, the root of the problem should be addressed before a fast because overeating, especially the wrong foods, after a fast is dangerous and can lead to death (if the fast was lengthy).
Fasting shouldn't be taken lightly, and there are many out there who don't do enough research beforehand to know what they're doing. Those with more knowledge should help others understand what is involved, and let them know if it is dangerous for their situation. Sure they need support, but support doesn't always include encouraging them to fast.