My experience has been that nobody gives a shit if you go to a restaurant in a group and order an explicitly vegetarian meal that isn't trying to emulate meat patties etc.
But they do care if you're trying to drag the entire friend group to a vegetarian restaurant.
In university, a group of friends once decided on heading out to dim sum for a celebration; one of them was Jewish, and ended up basically becoming a vegetarian for a day (since pork is all over the place in that cuisine). It was a source of lighthearted amusement for all and everyone was fully accommodating.
North American food culture doesn't depend on familiarity ("the same dish, just with the questionable thing substituted") at all. If anything, being a picky eater is discouraged and a sense of culinary adventure is praised. The service at QSRs has gotten slower in part because of pressure to reconfigure their basic ingredients into new, unfamiliar recipes. (Taco Bell is basically dedicated to this craft — and the greasy ground-beef slop doesn't even really look that different from the black bean slop anyway.)
Which is to say, it's not the meat eaters trying to impose culture on others. Vegetarians and vegans in my experience demonstrate an entirely unjustified persecution complex — the "they'll tell you" stereotype arises from the fact that people simply wouldn't care if it weren't explicitly brought up. That Simpson's episode with Lisa attempting vegetarianism was amusing, but also portrayed a world entirely alien to me.
Yes, North Americans eat a fair bit of meat on average. That's not at all the same thing as the dishes being "created around" the meat. We don't say "meatballs and spaghetti" (I even started automatically typing it the normal way around); substituting the meatballs for ground meat in the sauce is as natural as substituting a different shape of pasta.
Whole pieces of meat have a particular cachet, but this is because it's harder to hide a quality issue this way. Making a patty is missing the point. A hamburger is simply not highbrow cuisine. It's one culturally-established recipe, out of many, which is preferred in the context where it is mainly for convenience as finger food.
The proper vegetarian equivalent to a burger is a vegetarian wrap. (Or veggies on a bun, if the "bun form factor" is contextually important.) The proper vegetarian equivalent to a fancy meal with whole cuts of grilled meat is a fancy meal with artfully plated grilled vegetables.