In my case I have a 6 year old autistic son. Unlike a lot of children with autism that shy away from social situations, my son is overly social. For example, he will interact and talk with all people at all times. Walking in a mall he will go up to a stranger take their hand and walk off with them very happily. That being said I am planning on using a leash during our upcoming trip to Disney. For us it is a safety issue, yes I tend to get a lot of angry looks from people, but my son absolutely does not understand and can not grasp the concept of strangers and he will run off in an instant if anything catches his attention, which at Disney World is everything. So I will happily take the annoyed looks from others knowing that my son is with me and safe, and just to hopefully put some minds at ease, my son is very happy to wear the leash it does not embarrass him at all. Then again it is a part of everyday life for us whenever we are in public.
Other peoples disgust concerns me about as much as the dust under my couch.