So you are going on a meal replacement diet with no actual food but then expect to return to a 'normal' diet once you reach the target weight?
you also want to sit in a restaurant and not eat because you will be on the diet?
Firstly. I think your relationship with food is bizarre and unhealthy.
secondly what system are you using? how many shakes and bars per day. If you had 3 shakes and 3 snack bars you could be taking in as little as 900cals a day. Way under the recommended lower limit for dieting.
Rethink the diet. Home made mixed veggie soup will be better than shakes. A min 5 veggie salad will be better than a snack bar. You need to change your eating habits to lose weight not ignore them/cover them with a shake only diet.
As to your original question. Yes, YABU to want to sit in a restaurant whilst others eat. Eating is a social thing and to sit there and not eat is normalising unhealthy food relationship and will make everyone feel awkward. They will feel bad that you are not eating, they wont feel comfortable to eat etc
should people support you? yes, absolutely but your friends also have a place to point out your diet choice is unhealthy because shakes only... its not a good option long term and there are far better dieting options available to you.