I've told a few people: my other half (obviously), my mum, a friend of mine that also has weight issues and the friend who did LL and recommended it to me.
I told all these people as I know they will not judge my diet, they will be supportive and I need some people to know and talk to them about it. I will tell others slowly, once I'm used to the diet myself. We're seeing friends this weekend, they asked us out for dinner, but I asked if it could just be a drink (as I can have water) - so I want to tell them why I changed the plans and why I wont be able to do meals for awhile, they are lovely so they will be supportive.
Luckily I work for myself, so I have no colleagues to badger me. I think that can sometimes be hard as you see them every day. I think that following the advice of missbiker is a good idea. On this diet your checked by a doc/nurse, so you know your healthy. Plus you have loads of support and you lose weight, it all seems good to me!
I hate it when people are judgemental, you're doing what is best for you. Stick to your guns and good luck with your diet!