saucy everyone would have been eating something though. OP is talking about eating nothing.
The thing is, it's not really relevant what anyone here would be comfortable with. It's whether your friends would be ok with it.
Personally, I would think it was weird and awkward. If I'm spending money to go out and enjoy myself I don't want any awkward social issues surrounding it, IYSWIM.
That said, I would suggest a coffee/drink in the pub instead so everyone could be included and catered to.
I don't think it's attention seeking but I do think it has potential to make people uncomfortable and you've no right to do that to your friends (in the nicest possible way).
These diets are very extreme so I think committing to one requires changes and sacrifices and this might be one of them. Presumably this is a short term thing?
As an aside, I think you're feeling defensive has made you a little snippy in some responses, possibly understandably, and maybe oversensitive to what posters are actually saying?