'PASTA CONTAINS EGGS/CANCEL THE CHEQUE' 
Has the OP come back at all?!
The anti-vegan police will obviously jump on this thread-perhaps OP should have written 'I didn't want an egg on my pasta AIBU' to get some more non-biased responses.
Personally am really shy of telling people I am vegan because of the awful things people say online about them (including in this thread)! I try to not make a fuss at all. Also I don't like eating in front of people generally, an issue I've had since childhood and unrelated to being vegan, but being vegan means everyone wants to have a good gawp at your food-sometimes because of curiosity, understandable of course and sometimes to try to find something 'eeeew' about it, the mere thought of which is making me anxious now! So yes, I am very much non-vocal regarding it unless I am with people who I am very comfortable with. If it comes up directly in conversation or is relevant to context (e.g. if I am invited to someone's house for dinner)yes, otherwise nobody would know. It's one of those like ' you can always tell when someone's had lip filler' no, you can tell the ones who've had it done so It's obvious!
You have probably met many vegans but how would you know they'd not told you if they hadn't? Do you know every political, religious, spiritual belief held by absolutely everyone you've ever met?
The restaurant are in the wrong and vegnaism is a red herring here. The egg is a 'feature' of the pasta dish given it is quite unusual. Some people may order it BECAUSE of the egg, and some people definitely won't order it because of the egg, perhaps due to being vegan, allergies or perhaps due to it being a bit weird, not feeling egg really goes with tomatoes, just not fancying it? Or not liking eggs, period see what I did there
It should have stipulated on the menu that the egg is included in the dish, for all these reasons. It is a main component, not a garnish, and a lot of people don't like eggs or only like them in certain things/cooked certain ways IME.
OP may have known that the restaurant doesn't use fresh pasta or perhaps neglected to think about the fact that some contains eggs, but again, that doesn't mean that even someone who LIKES eggs would knowingly order a pasta dish with one on, perhaps they just wouldn't want that? Also a pub, unless a very well-reputed one famous for its gourmet food, is not likely to keep fresh pasta in their kitchen.
Fresh pasta is expensive and goes off fairly quickly.
The pub is also daft for not specifying 'V' 'VE' 'GF' etc-they could gain more custom that way-if someone's choosing between venues and looks at the menu online 'Doens't appear to be anything I can have in that one, let's go to that one, I know I can eat there' but also, it saves time-avoiding customers having to ask waiting staff about the menu.
I don't think the comparisons to bird muck etc attract reasonable response but to many vegans, vegetarians and people who just HATE certain foods, said food is as gross to them as those things are. I certainly wouldn't eat something that had just had an egg scraped off it because even before being vegan I thought eggs were absolutely disgusting-my meat-eating DP wouldn't eat it either.
It should have said on the menu. Most menus I've encountered may not list all components of a dish, but they should at least say what the dish actually IS!