I'm raising my daughter as a vegetarian. I was raised vegetarian (and since gone vegan), so this was a deal breaker for me discussed long before pregnancy. (My husband does eat meat, but not at home).
In contrast to the person mentioned above, I am forever grateful to have been raised vegetarian. It makes perfect sense to me that my Mum wouldn't feed me something she's morally opposed to. Vegetarian food can be totally safe and nutritious, and for me personally it is easy to know what to feed a vegetarian child, because I've been one!
For the fussy eaters mentioned, I've found Quorn Roarsomes and Birds Eye Fishless fingers to fill the gap for beige breaded protein perfectly well, along with crispy tofu bites... and if we have fussy kids over who aren't used to vegetarian substitutes, I've done cheese pizza, waffles and beans/peas with great success!
For parties I certainly don't bring special/disappointing vegetarian food... I've not been to any kids parties that didn't have cheese sandwiches so far, and usually lots of other options like jam sandwiches, egg sandwiches, cheese pizza, plus fruit, houmous, bread sticks, vegetable sticks, crisps, party rings, jelly pots, jammie dodgers... most party food is fine! The only effort required so far has been occasionally swapping out party bag haribo for the vegetarian equivalent... but I already check party bags for hard lollies and swap those out, so it's not a lot of extra trouble!
She's welcome to make a different choice when she's older (my brother and I completely diverged - he took up meat eating and I went vegan!), but until then she's stuck with what I believe is right... same with vaccinations (yes), extended rear facing, a blanket ban on Bing and a strict policy on choking hazards!