Again, all I can tell you is how I've dealt with telling people - and it isn't for everyone. I've told everyone about the diet, but I did loads of research into the science and statistics first, and if anyone asks I sort of bore them into submission with a barrage of information. A 'don't f@ck with me' expression probably helps too, if I'm honest. But it's genuinely been my experience that people are really happy for me cos I'm losing weight, they know I've gone into it from an informed position and, while they may be sceptical behind my back, they're showing support and acceptance.
It might be different if I was dieting from a size 12 to a ten, people can be jealous. But I was a size 24, and I haven't had a single negative person.
Oh, also - what tends to shut people up is if I say "my doctor won't refer me for tests until I'm under bmi 30". The tests could be for anything. Menstrual anomalies, IBS, sleep disorders...